http://www.researchonline.mq.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:25052 To quantify the aggregrate losses from operational risk, we employ an actuarial risk model, ie, we consider compound Cox model of operational risk to deal with the stochastic nature of its frequency rate in real solutions. A shot noise process is used for this purpose. A compound Poisson model is also considered as its countrepart for the case where the operational loss frequency rate is deterministic. As the loss amounts arising due to mismanagement of operational risks are extremes in practice, we assume the loss sizes are log gamma, Frechet and truncated Gumbel. We also use an exponential distribution for the case of non-extreme losses. Employing a loss distribution approach, we derive the analytical/explicit forms of the Laplace transform of the distribution of aggregate operational losses. The value-at-risk and tail conditional expectation are used to evaluate the operational risk capital charge. Fast Fourier transform is used to approximate VaR and TCE numerically and the figures of the distributions of aggregate operational losses are provided. Numerical comparisons of VaR and TCE obtained using two compound processes are also made. 2013-04-02T23:21:50.198Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24876 In this article, the author responds to the research paper by Sashi Sharma titled "Exploring Pre-Service Teachers' Understanding of Statistical Variation: Implications of Teaching and Research." According to the author, Sharma describes a study designed to investigate pre-service teachers' acknowledgment of variation in sampling and distribution environments. He observes that a survey conducted by Sharma did not indicate that its purpose was to assess understanding of variation. He clarifies that his comments are not meant to detract from the aims and methods of Sharma's paper. 2013-03-20T11:11:13.175Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24889 This paper develops a valuation model for a perpetual convertible bond when the price dynamics of the underlying share are governed by continuous-time Markovian regime-switching models. We suppose that the appreciation rate and the volatility of the underlying share are modulated by a continuous-time, finite-state, observable Markov chain. The states of this chain are interpreted as the states of an economy. Here the valuation problem of the perpetual convertible bond can be viewed as that of valuing a perpetual stock loan, or a perpetual American option with time-dependent strike price. With the presence of the regime-switching effect, the market in the model is, in general, incomplete. To provide a convenient method to determine a price kernel for valuation, we employ the regime-switching Esscher transform introduced in Elliott, Chan and Siu (2005). We then adopt the differential equation approach in Guo and Zhang (2004) to solve the optimal stopping problem associated with the valuation of the perpetual convertible bond. Numerical examples are presented to illustrate the practical implementation of the proposed model. 2013-03-20T11:10:24.567Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24774 For the additive risk model with time-varying covariates which are subject to measurement errors, we study the estimation of both regression parameters and cumulative baseline hazard function. We first develop a procedure to estimate the regression parameters by correcting the bias of the naive estimator, and provide the large-sample properties of the bias-adjusted estimators. The procedure can be repeated to further improve the accuracy of the estimator. We then construct a corresponding estimator for the cumulative baseline hazard function and derive its asymptotic properties. Based on these results, confidence bands are constructed for the cumulative hazard function as well as the survival function. Monte Carlo studies are conducted to evaluate the performance of these estimators. 2013-03-13T09:50:42.069Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24775 Applying the piecewise derteministic processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance. 2013-03-13T09:50:36.698Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24645 The Esscher transform is an important tool in actuarial science. Since the pioneering work of Gerber and Shiu (1994), the use of the Esscher transform for option valuation has also been investigated extensively. However, the relationships between the asset pricing model based on the Esscher transform and some fundamental equilibrium-based asset pricing models, such as consumption-based models, have so far not been well-explored. In this paper, we attempt to bridge the gap between consumption-based models and asset pricing models based on Esscher-type transformations in a discrete-time setting. Based on certain assumptions for the distributions of asset returns, changes in aggregate consumptions and returns on the market portfolio, we construct pricing measures that are consistent with those arising from Esscher-type transformations. Explicit relationships between the market price of risk, and the risk preference parameters are derived for some particular cases. 2013-03-11T21:11:22.288Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24668 In this paper we propose a semiparametric model to fit medical cost data with a proportion of zero cost values. In our model, the unknown cumulative cost is defined to be a function of the failure time to account for the correlation between the cost and the failure time. The nonparametric nature of the cost function allows full flexibility in matching the reality. Local likelihood estimation is proposed to estimate the unknown accumulative cost functions and the related parameters, and their asymptotic properties are investigated as well. Simulation studies are performed to illustrate our models and proposed methods. 2013-03-11T21:10:37.448Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24669 We study stochastic scheduling on m parallel identical machines with random processing times. The cost involved in the problem is discounted to the present value and the objective is to minimize the expected discounted holding cost, which covers in a unified framework many performance measures discussed in the literature as special cases, including discounted rewards, flowtime, and makespan. We prove that the SEPT rule is optimal, on a fairly general ground, in the class of preemptive dynamic policies, the class of nonpreemptive dynamic policies, and the class of nonpreemptive static list policies. The LEPT rule, on the other hand, is optimal to minimize the expected discounted makespan only under certain restrictive conditions. Without such conditions, the LEPT rule is found no longer optimal for discounted makespan by a counterexample, in contrast to the case without discounting. 2013-03-11T21:10:34.403Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24670 Motivated by a practical problem, [Z.W. Cai, P.A. Naik, C.L. Tsai, De-noised least squares estimators: An application to estimating advertising effectiveness, Statist. Sinica 10 (2000) 1231–1243] proposed a new regression model with noised variables due to measurement errors. In this model, the means of some covariates are nonparametric functions of an auxiliary variable. They also proposed a de-noised estimator for the parameters of interest, and showed that it is root-n consistent and asymptotically normal when undersmoothing is applied. The undersmoothing, however, causes difficulty in selecting the bandwidth. In this paper, we propose an alternative corrected de-noised estimator, which is asymptotically normal without the need for undersmoothing. The asymptotic normality holds over a fairly wide range of bandwidth. A consistent estimator of the asymptotic covariance matrix under a general stationary error process is also proposed. In addition, we discuss the fitting of the error structure, which is important for modeling diagnostics and statistical inference, and extend the existing error structure fitting method to this new regression model. A simulation study is made to evaluate the proposed estimators, and an application to a set of advertising data is also illustrated. 2013-03-11T21:10:33.098Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24672 In this paper, we study the estimation of the unbalanced panel data partially linear models with a one-way error components structure. A weighted semiparametric least squares estimator (WSLSE) is developed using polynomial spline approximation and least squares. We show that the WSLSE is asymptotically more efficient than the corresponding unweighted estimator for both parametric and nonparametric components of the model. This is a significant improvement over previous results in the literature which showed that the simply weighting technique can only improve the estimation of the parametric component. The asymptotic normalities of the proposed WSLSE are also established. Another focus of this paper is to provide a variable selection procedure to select significant covariates in the parametric part, based on a combination of the nonconcave penalization and the weighted semiparametric least squares. The proposed procedure simultaneously selects significant covariates and estimates unknown parameters. With a proper choice of regularization parameters and penalty function, the resulted estimator is shown to possess an oracle property. Simulation studies and an example of application on a set of hormone data are used to demonstrate this proposed procedure. 2013-03-11T21:10:28.338Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24673 Change-point hazard models have been extensively investigated by many authors, but the literature on change-point problems with survival data subject to censoring is rather small. In an earlier example provided by Matthews and Farewell (1982), a set of nonlymphoblastic leukemia data were fitted by using a change-point model. But for that data set, the Kaplan-Meier estimator of the distribution function levels off well below 1, which indicates the presence of "long-term survivors" in the data. In this paper, we propose a new change-point model for survival data that accounts for long-term survivors. Estimation methods for the proposed model are investigated, and large-sample properties of the estimators are established. A simulation study is carried out to evaluate the performance of the estimating methods. As an application, the nonlymphoblastic leukemia data are re-analyzed using the new model. 2013-03-11T21:10:26.004Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24676 26 page(s) 2013-03-11T21:10:19.553Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24681 Discussion of Phelim Boyle and Sun Siang Liew's "Asset Allocation with Hedge Funds on the Menu" (NAAJ Volume 11, Number 4, December 2007) 2013-03-11T21:10:08.277Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:24572 This study examines on the basis of economic theory the determinants of exchange rate volatilities for a large number of currencies. We relate daily changes in GARCH(1,1) volatilities of exchange rates to the volatility changes of several of their presumed fundamental economic determinants in the context of a portfolio balance model. The use of high-frequency data limits the choice of the explanatory economic variables that can be included in empirical estimates. The first differences of GARCH(1,1) volatilities of share and bond price indices reflect portfolio trading decisions in corresponding markets for both assets. In the same vein, first differences of the gold price volatility, as an additional determinant, are related to exchange rate volatilities of two commodity currencies in the sample. The panel data estimates, using the Seemingly Unrelated Regression technique, produce coefficients with the expected signs and statistical significance. The results of our study enhance our understanding of high-frequency currency volatility changes for 19 currencies beyond the purview of announcement effects in the event studies framework. 2013-03-06T08:01:28.038Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15138 A risk minimization problem is considered in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, finite-state, Markov chain. We interpret the states of the chain as different states of an economy. A particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a measure of risk and an optimal portfolio is determined by minimizing the convex risk measure of the terminal wealth. We explore the state of the art of the stochastic differential game to formulate the problem as a Markovian regime-switching version of a two-player, zero-sum, stochastic differential game. A novel feature of our model is that we provide the flexibility of controlling both the diffusion risk and the regime-switching risk. A verification theorem for the Hamilton–Jacobi–Bellman (HJB) solution of the game is provided. 2012-04-04T05:50:17.534Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:18275 Relatively little research has explored the personality types and interests of actuaries: the sole published study profiled North American actuaries using the Myers Briggs Type Indicator and the Strong Interest Inventory. In contrast, a number of studies of accountants have shown a clear and consistent dominance of certain personality preferences, with some authors expressing concern about the implied narrowness of the accounting profession and the possible lack of certain valued skills such as strategic thinking and persuasive communication. Personality type has been shown to be related to management, leadership and decision–making style; for example, it has been suggested that the dominance of Sensing / Concrete types in the accounting profession as a whole does not apply to those at the higher levels, who are predominantly Intuitive / Conceptual. This paper reviews what is known of the personality types of actuaries and contrasts the profiles of actuaries and accountants. The links between personality type and job satisfaction, leadership and management are explored. Finally, scope for further research and implications for the actuarial profession are highlighted. 2012-03-23T00:10:08.628Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7497 For insurance risks, jump processes such as homogeneous/non-homogeneous compound Poisson processes and compound Cox processes have been used to model aggregate losses. If we consider the economic assumption of a positive interest to aggregate losses, Lévy processes have proven to be useful. Also in financial modelling, it has been observed that diffusion models are not robust enough to capture the appearance of jumps in underlying asset prices and interest rates. As a result, jump diffusion processes, which are, simply speaking, combinations of compound Poisson processes with Brownian motion, have gained popularity for modelling in insurance and finance. In this paper, considering a jump diffusion process, we obtain the explicit expression of the joint Laplace transform of the distribution of a jump diffusion process and its integrated process, assuming that jump size follows the mixture of two exponential distributions, which is a special case of phase-type distributions. Based on this Laplace transform, we derive the moments of the aggregate accumulated claim amounts of insurance risk. For a financial application, we concern non-defaultable zero-coupon bond pricing. We also provide several numerical examples for the moments of aggregate accumulated claims and default-free zero-coupon bond prices. 2012-03-22T05:47:27.062Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:377 The Lee-Carter method for mortality forecasting is outlined, discussed and improved utilizing standard time series approaches. The new framework, which integrates estimation and forecasting, delivers more robust results and permits more detailed insight into underlying mortality dynamics. An application to women's mortality data illustrates the methods. 2012-03-21T05:00:39.416Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:6729 We consider the valuation of participating life insurance policies using a regime-switching Esscher transform developed in Elliott, Chan and Siu (2005) when the market values of the reference asset are driven by a Markov-modulated geometric Brownian motion (GBM). We employ the Markov-modulated GBM driven by a continuous-time hidden Markov chain model to describe the impact of the switching behavior of the states of economy on the price dynamics of the reference asset. We also explore the change of measures technique to reduce the dimension of the valuation problem. 2012-02-14T22:02:25.844Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:17375 This paper describes the causes of the collapse of the Penn Square Bank in 1982, and the flow on effects to the US financial system - that is, it examines the systemic risk factors. The paper makes comparisons to the current US banking crisis, and in particular points out the similaritis between Penn Square and Indymac. 2012-02-06T18:21:10.874Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:1072 This paper deals with the methodology of liability forecasting using the runoff triangle data. Techniques are based on time series models and methods that facilitate the calculation of forecast distributions and the assessment of model fit. The models deal with correlation within triangles. Correlations are critical to proper reserving. The output of the methodology is the complete shape of the liability distribution. Methods are applied to a well-known runoff triangle and results compared to those from previous studies. 2012-01-23T22:00:20.917Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16815 Using an actuarial model, we examine the cost of delay in mortgage/credit loan payments. It is assumed that the default arrival process follows the Poisson process and the loss sizes are assumed to be independent and an identical truncated exponential. We also assume that the delay between default occurrence and partially (or fully) recovered payment is an independent identical truncated exponential random variable. For the recovery rate random variable, we simply use its expectation. Using the relationship between the shot noise process and accumulated/discounted aggregate losses process and applying the piecewise deterministic Markov processes theory, we obtain the explicit expressions for the expected value of losses and the expected value of part (or whole) of the loan recovered with the delay. Based on these moments, we define and predict the cost of delay in a mortgage/credit loan portfolio and their numerical examples are provided. 2012-01-11T10:41:25.813Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16822 Using an optimizing financial planning model in the tradition of Merton and Richard we explore how individuals should determine their life insurance and annuity choices, given uncertainty about investment returns and mortality. Both consumption and bequests appear as arguments in the individual's preference function. The model explicitly recognizes the existence of social security in retirement, and of loadings on insurance premiums, due to administration costs in the life insurance and annuities markets. The model sheds light on the reasons for the thinness of voluntary life annuity markets worldwide. The relative importance of pre-existing annuitization through social security, the role of bequests, and premium loadings are quantitatively assessed within a single optimizing framework. Results are presented for a model specification calibrated to Japan. 2012-01-11T10:41:08.218Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16158 Recurrent event data arise frequently from medical research. Examples include repeated infections, recurrence of tumors, relapse of leukemia, repeated hospitalizations, recurrence of symptoms of a disease, and so on. In the analysis of recurrent event data, the proportional rates model assumes that the regression coefficients are time invariant. In reality, however, these parameters may vary over time, and the temporal covariate effects on the event process are of great interest. In this article, we formulate a class of semiparametric marginal rates models, which incorporate a mixture of time-varying and time-independent parameters, to analyze recurrent event data. For statistical inference on model parameters, an estimation procedure is developed and asymptotic properties of the proposed estimators are established. In addition, we develop tests for investigating whether or not covariate effects vary with time. The finite-sample behaviors of the proposed methods are examined in simulation studies. An example of application of the proposed methodology is illustrated on a set of data from a clinic study on chronic granulomatous disease. 2011-11-29T08:00:23.763Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16128 For premium calculation principles or risk measures, all existing works only consider the additivity for a finite number of comonotonic risks. As we all know, a limiting status of finite additivity is the additivity for countable risks. In this paper we investigate the countable additivity and generate new and elegant characterizations for Choquet pricing and distortion premium principles. We also study the countable exchangeability, as an extension to additivity. It leads to generalized Choquet pricing and generalized distortion premium principles. 2011-11-28T10:00:30.968Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16131 In classical Bühlmann credibility models, claims are assumed to be independent between different risks. In many practical situations, however, this assumption may be violated because there are situations that could drive possible relationship among the insured individuals. This paper aims to extend the Bühlmann and Bühlmann–Straub credibility models to account for a special type of dependence between risks induced by common stochastic effects. By means of the projection method, the corresponding credibility premiums are obtained, which generalize some well known existing results in credibility theory. 2011-11-28T10:00:23.256Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16133 The estimation of loss reserves for incurred but not reported (IBNR) claims presents an important task for insurance companies to predict their liabilities. Conventional methods, such as ladder or separation methods based on aggregated or grouped claims of the so-called “run-off triangle”, have been illustrated to have some drawbacks. Recently, individual claim loss models have attracted a great deal of interest in actuarial literature, which can overcome the shortcomings of aggregated claim loss models. In this paper, we propose an alternative individual claim loss model, which has a semiparametric structure and can be used to fit flexibly the claim loss reserving. Local likelihood is employed to estimate the parametric and nonparametric components of the model, and their asymptotic properties are discussed. Then the prediction of the IBNR claim loss reserving is investigated. A simulation study is carried out to evaluate the performance of the proposed methods. 2011-11-28T10:00:21.641Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16135 This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies, and extends existing disparate approaches discussed in the literature. Analytical and computer generated illustrations are given as well as suggestions for the practical determination of aversion functions. 2011-11-28T10:00:17.966Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10808 We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black–Scholes–Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem. 2011-11-28T04:22:21.844Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15435 In this paper we use Ching's multivariate Markov chain model to model the dependency of rating transitions of several credit entities. The model is an enhancement of the multivariate Markov chain model for ratings considered by Siu et al. Our model is more parsimonious, flexible and empirically competent than the model used by Siu et al. We adopt an efficient method to calibrate the model parameters and formulate the estimation problem as a linear programming problem that can easily be solved using spreadsheets. We compare the estimation results and the computational efficiency of the enhanced model with that of Siu et at. We also empirically investigate the effect of incorporating both positive and negative associations on portfolio credit risks. 2011-10-17T04:10:55.538Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15364 A risk minimization problem is considered in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, finite-state Markov chain. We interpret the states of the chain as different market regimes. A convex risk measure is used as a measure of risk and an optimal portfolio is determined by minimizing the convex risk measure of the terminal wealth. We explore the state of the art of the stochastic differential game to formulate the problem as a Markovian regime-switching version of a two-player, zero- sum stochastic differential game. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided. 2011-10-11T17:50:15.119Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15351 Purpose: This research analyses the joint behaviour of mortality in different populations, and aims to model their difference and similarities using a joint model. Originality: Existing mortality studies typically analyse single populations with each population analysed separately and without reference to other populations. Such an approach limits the pooling of common trend and cross sectional information across populations and limits the ability to discern and understand differences between populations. This research aims to develop “joint” mortality model based on the Lee-Carter framework. The multiple population framework permits detailed analyses of differences and co-integration behaviour. Key literature / theoretical perspective: The extended framework employs the Lee-Carter model as the building block, and extends a single population Least Squares Estimation method (SLSE) to a Multiple population format (MLSE). Design/methodology/approach: This research firstly deduces the MLSE framework, and then analyses data from different and similar populations. Therefore, is will focus on theoretical deduction and quantitative analysis. Findings: Similarities across populations are specified as restrictions and are tested. Combining populations makes for more efficient forecasting and the analysis and understanding of divergent trends in different populations. Research limitations/implications: Restrictions are not easy to establish, and reasons for differences may be complex and not simply quantified. Practical and Social implications: This research may lead to theoretical developments that will increase the accuracy of mortality projection. Furthermore, if a population is too small to be estimated, or its data is not reliable, it can be forecast by reference to a highly similar population. 2011-10-11T02:50:12.077Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15257 Recently Markov-modulated compound Poisson models have gained its popularity in modelling insurance claims in the actuarial science literature. A Markov-modulated compound Poisson model can provide a realistic and flexibile way to model aggregate insurance claims by incorporating the impact of hidden states of an economy on claim frequencies and claim sizes. However, in practice, the Markov chain in the model is not observable. It is of practical interest to develop some methods to estimate the hidden state of the Markov chain and other unknown model parameters of the Markov- modulated compound Poisson model. This paper considers this important issue. We shall develop filters and smoothers for the hidden state of the economy underlying the Markov-modulated compound Poisson model. In general, we consider the case when both the stochastic intensity and the distribution of the claim sizes of the compound Poisson process depend on the hidden Markov chain. The filter and smoother provide an optimal way to estimate the insurance claims model in the "mean- squared-error" sense. We shall also develop estimators for the unknown model parameters of the Markov-modulated marked point process using the robust filter-based and smoother-based EM algorithms. 2011-10-06T04:40:44.343Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15219 We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two-stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant. 2011-10-05T13:11:24.590Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15222 In this paper, we introduce a High-order Markov-Switching (HMS) model for measuring the risk of a portfolio. We suppose that the rate of return from a risky portfolio follows an HMS model with the drift and the volatility modulated by a discrete-time weak Markov chain. The states of the weak Markov chain are interpreted as observable states of an economy. We adopt the Value-at-Risk (VaR) as a metric for market risk quantification and examine the high-order effect of the underlying Markov chain on the risk measures via backtesting. 2011-10-05T13:11:20.541Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15223 We investigate an optimal portfolio selection problem in a continuous-time Markov-modulated financial market when an economic agent faces model uncertainty and seeks a robust optimal portfolio strategy. The key market parameters are assumed to be modulated by a continuous-time, finite-state Markov chain whose states are interpreted as different states of an economy. The goal of the agent is to maximize the minimal expected utility of terminal wealth over a family of probability measures in a finite time horizon. The problem is then formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game between the agent and the market. We solve the problem by the Hamilton-Jacobi-Bellman approach. 2011-10-05T13:11:17.462Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15224 We consider the bond valuation problem when the short rate process is described by a Markovian regime-switching Hull–White model or a Markovian regime-switching Cox– Ingersoll–Ross model. In each of the two short rate models, we establish a Markov-modulated exponential-affine bond price formula with coefficients given in terms of fundamental matrix solutions of linear matrix differential equations. 2011-10-05T13:11:16.773Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15225 Although its drawbacks are well known, VAR has become institutionalised as the market risk measure of choice among trading firms and regulators. Now there is a growing feeling that a reappraisal is overdue, exemplified here by Phelim Boyle, Tak Kuen Siu and Hailiang Yang. Using the example of an unhedged option position in the classic two-level binomial tree framework, they evaluate VAR and alternative risk measures using objective and subjective probability measures. 2011-10-05T13:11:13.721Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15228 We derive a martingale representation for a contingent claim under a Markov-modulated version of the Black-Scholes economy. The martingale representation for the price of the claim is established with respect to an equivalent martingale measure chosen by the Esscher transform. Under some differentiability conditions for the coefficients of the price processes, we shall identify explicitly the integrands in the martingale representation using stochastic flows. We shall introduce a zero-coupon bond to minimize the residual risk due to incomplete hedging. 2011-10-05T13:11:09.561Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15230 In this paper, we propose an Interactive hidden Markov model (IHMM). In a traditional HMM, the observable states are affected directly by the hidden states, but not vice versa. In the proposed IHMM, the transitions of hidden states depend on the observable states. We also develop an efficient estimation method for the model parameters. Numerical examples on the sales demand data and economic data are given to demonstrate the applicability of the model. 2011-10-05T13:11:05.510Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15231 In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one of the regimes described by the states of an observable Markov chain process. By augmenting the conditional Esscher transform with the observable Markov switching process, a Markov switching conditional Esscher transform (MSCET) is developed to identify a martingale measure for option valuation in the incomplete market described by our model. We provide an alternative approach for the derivation of an analytical option valuation formula under the Markov switching Heston-Nandi GARCH (1, 1) model. The use of the MSCET can be justified by considering a utility maximization problem with respect to a power utility function associated with the Markov switching risk-averse parameters. 2011-10-05T13:11:01.489Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15233 We introduce a class of Bayesian infinite mixture models first introduced by Lo (1984) to determine the credibility premium for a non-homogeneous insurance portfolio. The Bayesian infinite mixture models provide us with much flexibility in the specification of the claim distribution.We employ the sampling scheme based on a weighted Chinese restaurant process introduced in Lo et al. (1996) to estimate a Bayesian infinite mixture model from the claim data. The Bayesian sampling scheme also provides a systematic way to cluster the claim data. This can provide some insights into the risk characteristics of the policyholders. The estimated credibility premium from the Bayesian infinite mixture model can be written as a linear combination of the prior estimate and the sample mean of the claim data. Estimation results for the Bayesian mixture credibility premiums will be presented. 2011-10-05T13:10:57.846Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15235 The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discretetime version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the lognormal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted. 2011-10-05T13:10:53.927Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15237 This paper proposes the use of Bayesian approach to implement Value at Risk (VaR) model for both linear and non-linear portfolios. The Bayesian approach provides risk traders with the flexibility of adjusting their VaR models according to their subjective views. First, we deal with the case of linear portfolios. By imposing the conjugate-prior assumptions, a closed-form expression for the Bayesian VaR is obtained. The Bayesian VaR model can also be adjusted in order to deal with the ageing effect of the past data. By adopting Gerber-Shiu's option-pricing model, our Bayesian VaR model can also be applied to deal with non-linear portfolios of derivatives. We obtain an exact formula for the Bayesian VaR in the case of a single European call option. We adopt the method of back-testing to compare the non-adjusted and adjusted Bayesian VaR models with their corresponding classical counterparts in both linear and non-linear cases. 2011-10-05T13:10:48.940Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15238 Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided. 2011-10-05T13:10:44.309Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15240 15 page(s) 2011-10-05T13:10:43.216Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15241 This paper defines risk measure in a measure-theoretic framework and shows how some common risk measures can be interpreted using that definition. 2011-10-05T13:10:40.004Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15242 We consider the pricing of both fixed rate and floating rate risky debts when the value of a firm is governed by a Markov-modulated generalized jump-diffusion model with the jump component described by a completely random measure process with a Markov-switching compensator; that is, the compensator switches over time according to the states of an economy modelled by a continuous-time Markov chain. We shall employ the well-known tool in actuarial science, namely, the Esscher transform, to determine the price of the risky debts. We shall investigate consequences for the prices of the risky debts of various parametric specifications of the jump component. Sensitivity analysis for the prices of the risky debts with respect to various model parameters will be conducted. We also compare the pricing results obtained from our model with those from the celebrated Merton jump-diffusion model to illustrate the effect of correlated jump times and sizes on the prices of the debts. 2011-10-05T13:10:39.172Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15139 This paper introduces nonparametric Bayesian credibility without imposing stringent parametric assumptions on claim distributions. We suppose that a claim distribution associated with an unknown risk characteristic of a policyholder is an unknown parameter vector with infinite dimension. In this way, we incorporate the uncertainty of the functional form of the claim distribution associated with the unknown risk characteristic in calculating credibility premiums. Using the results of Ferguson (1973), formulas of the Bayesian credibility premiums are obtained. The formula for the Bayesian credibility pure premium is a linear combination of the overall mean and the sample mean of the claims. This is consistent with the result in the classical credibility theory. We perform a simulation study for the nonparametric Bayesian credibility pure premiums and compare them with the corresponding Bühlmann credibility premiums. Estimation results for the credibility premiums using Danish fire insurance loss data are presented. 2011-09-29T06:50:46.106Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15140 In this paper, we first introduce the use of an interactive hidden Markov model (IHMM) for modeling and analyzing default data in a sector. Under the IHMM, transitions of the hidden risk states of the sector depend on the observed number of bonds in the sector that default in the current time period. This incorporates the feedback effect of the number of defaults on the transitions of the hidden risk states. This feature seems to be more realistic and does not enjoy by the traditional HMMs. We then develop a “dynamic” version of the binomial expansion technique (BET) modulated by the IHMM for modeling the occurrence of defaults of bonds issued by firms in the same sector. Under the BET modulated by the IHMM, the number of bonds defaulting in each time period follows a Markov-modulated binomial distribution with the probability of defaulting of each bond depending on the states of the IHMM, which represent the hidden risk states of the sector. Efficient method will be presented for estimating the model parameters in the BET modulated by the IHMM. We shall compare the hidden risk state process extracted from the IHMM-modulated BET with that extracted from the BET modulated by HMM in order to illustrate the significance of the feedback effect using real data. We shall also present the estimation results for the BET modulated by the IHMM and compare them with those for the BET modulated by the HMM. 2011-09-29T06:50:43.166Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15141 We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems. 2011-09-29T06:50:42.205Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15033 We consider the valuation of credit default swaps (CDSs) under an extended version of Merton’s structural model for a firm’s corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm’s value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm’s value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation. 2011-09-23T14:20:43.770Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15034 In this paper, we consider a game theoretic approach to option valuation under Markovian regime-switching models, namely, a Markovian regime-switching geometric Brownian motion (GBM) and a Markovian regime-switching jump-diffusion model. In particular, we consider a stochastic differential game with two players, namely, the representative agent and the market. The representative agent has a power utility function and the market is a “fictitious” player of the game. We also explore and strengthen the connection between an equivalent martingale measure for option valuation selected by an equilibrium state of the stochastic differential game and that arising from a regime switching version of the Esscher transform. When the stock price process is governed by a Markovian regime-switching GBM, the pricing measures chosen by the two approaches coincide. When the stock price process is governed by a Markovian regime-switching jump-diffusion model, we identify the condition under which the pricing measures selected by the two approaches are identical. 2011-09-23T14:20:41.746Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15035 This paper considers a partial differential equation (PDE) approach to evaluate coherent risk measures for derivative instruments when the dynamics of the risky underlying asset are governed by a Markov-modulated geometric Brownian motion (GBM); that is, the appreciation rate and the volatility of the underlying risky asset switch over time according to the state of a continuous-time hidden Markov chain model which describes the state of an economy. The PDE approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markov-modulated Black–Scholes model. We shall derive the PDEs satisfied by the risk measures for European-style options, barrier options and American-style options. 2011-09-23T14:20:40.334Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15036 In this paper, we develop an option valuation model when the price dynamics of the underlying risky asset is governed by the exponential of a pure jump process specified by a shifted kernel-biased completely random measure. The class of kernel-biased completely random measures is a rich class of jump-type processes introduced in [James, L.F., 2005. Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages. Ann. Statist. 33, 1771–1799; James, L.F., 2006. Poisson calculus for spatial neutral to the right processes. Ann. Statist. 34, 416–440] and it provides a great deal of flexibility to incorporate both finite and infinite jump activities. It includes a general class of processes, namely, the generalized Gamma process, which in its turn includes the stable process, the Gamma process and the inverse Gaussian process as particular cases. The kernel-biased representation is a nice representation form and can describe different types of finite and infinite jump activities by choosing different mixing kernel functions. We employ a dynamic version of the Esscher transform, which resembles an exponential change of measures or a disintegration formula based on the Laplace functional used by James, to determine an equivalent martingale measure in the incomplete market. Closed-form option pricing formulae are obtained in some parametric cases, which provide practitioners with a convenient way to evaluate option prices. 2011-09-23T14:20:38.180Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15037 This paper introduces the class of Bayesian infinite mixture time series models first proposed in Lau & So (2004) for modelling long-term investment returns. It is a flexible class of time series models and provides a flexible way to incorporate full information contained in all autoregressive components with various orders by utilizing the idea of Bayesian averaging or mixing. We adopt a Bayesian sampling scheme based on a weighted Chinese restaurant process for generating partitions of investment returns to estimate the Bayesian infinite mixture time series models. Instead of using the point estimates, as in the classical or non-Bayesian approach, the estimation in this paper is performed by the full Bayesian approach, utilizing the idea of Bayesian averaging to incorporate all information contained in the posterior distributions of the random parameters. This provides a natural way to incorporate model risk or uncertainty. The proposed models can also be used to perform clustering of investment returns and detect outliers of returns. We employ the monthly data from the Toronto Stock Exchange 300 (TSE 300) indices to illustrate the implementation of our models and compare the simulated results from the estimated models with the empirical characteristics of the TSE 300 data. We apply the Bayesian predictive distribution of the logarithmic returns obtained by the Bayesian averaging or mixing to evaluate the quantile-based and conditional tail expectation risk measures for segregated fund contracts via stochastic simulation. We compare the risk measures evaluated from our models with those from some well-known and important models in the literature, and highlight some features that can be obtained from our models. 2011-09-23T14:20:36.586Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:15038 We investigate the ruin probability when the surplus process is governed by a generalized perturbed risk model with a Markov-switching compensator. We suppose that the jump component of the perturbed risk model is specified by a completely random measure process with the compensator switching over time according to the states of an economy described by a continuous-time hidden Markov chain model. Accordingly, we assume that the force of interest, the rate of premium and the diffusion volatility rate switch over time according to the states of the economy. A simulation experiment will be conducted. 2011-09-23T14:20:34.437Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:14456 7 page(s) 2011-08-11T04:50:22.053Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9760 We investigate the problem of scheduling a set of jobs to minimize the expected makespan or the variance of the makespan. The jobs are subject to deteriorations which are expressed as linear increments of the processing requirements. The machine is subject to preemptive-resume breakdowns with exponentially distributed uptimes and downtimes. It has been well known in the classical models that the expectation and variance of the makespan of deteriorating jobs can be minimized analytically by an index policy if no machine breakdowns are involved. Such basic features, however, change dramatically when breakdowns and deteriorations are present together. In this paper, we derive conditions for jobs to be processible in the sense that they will be eventually completed, and the characteristics of the time that a job occupies the machine. We further find that the expected makespan can still be minimized by a simple index policy that is independent of the breakdown process, but this is no longer the case for the variance of the makespan. 2011-06-23T00:05:01.196Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12740 This paper is to study nonparametric Bayesian estimation for a proportional hazards model with "long-term survivors". The cumulative hazards function is modeled by a beta process, and the priors of the cure rate and coefficient of covariates can be improper distributions under the proposed model. The posterior estimators of the cure rate, the coefficient for covariates and the survival function are estimated from the cases of discrete-time, continuous-time and grouped survival data. A set of leukemia data are re-analyzed to illustrate the proposed model and statistical inference via a Markov chain Monte Carlo (MCMC) algorithm with Gibbs sampling. 2011-05-25T22:03:02.655Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12219 We investigate two approaches, namely, the Esscher transform and the extended Girsanov’s principle, for option valuation in a discrete-time hidden Markov regime-switching Gaussian model. The model’s parameters including the interest rate, the appreciation rate and the volatility of a risky asset are governed by a discrete-time, finite-state, hidden Markov chain whose states represent the hidden states of an economy. We give a recursive filter for the hidden Markov chain and estimates of model parameters using a filter-based EM algorithm. We also derive predictors for the hidden Markov chain and some related quantities. These quantities are used to estimate the price of a standard European call option. Numerical examples based on real financial data are provided to illustrate the implementation of the proposed method. 2011-03-21T05:02:11.865Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12216 This paper is concerned with the statistical inference on seemingly unrelated varying coefficient partially linear models. By combining the local polynomial and profile least squares techniques, and estimating the contemporaneous correlation, we propose a class of weighted profile least squares estimators (WPLSEs) for the parametric components. It is shown that the WPLSEs achieve the semiparametric efficiency bound and are asymptotically normal. For the non-parametric components, by applying the undersmoothing technique, and taking the contemporaneous correlation into account, we propose an efficient local polynomial estimation. The resulting estimators are shown to have mean-squared errors smaller than those estimators that neglect the contemporaneous correlation. In addition, a class of variable selection procedures is developed for simultaneously selecting significant variables and estimating unknown parameters, based on the non-concave penalized and weighted profile least squares techniques. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures perform as efficiently as if one knew the true submodels. The proposed methods are evaluated using wide simulation studies and applied to a set of real data. 2011-03-21T05:02:11.603Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12217 Two-sample comparison of survival times with “cured patients” is of major interest and a challenging issue in many areas, particularly in cancer clinical research. Recently, several authors have proposed various procedures of comparison, including tests of no overall, no short-term and no long-term differences between two samples. In clinical practice, it is often of interest to detect the difference in treatment effects among noncured patients regardless of the difference between cure fractions. In this paper, we propose a statistical test to compare two samples with cured patients and possibly heterogeneous treatment effects based on a class of semi-parametric transformation models, and our main focus is on the survival times of noncured patients. The empirical and quantile processes are used to construct strong approximations for the empirical curves. The two-sample test is then constructed from general least squares estimators derived from these processes. Simulation results show that the proposed test perform well. As an example of application, a set of bladder cancer data is analyzed to illustrate the proposed methods. 2011-03-21T05:02:07.839Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12218 Semiparametric transformation model has been extensively investigated in the literature. The model, however, has little dealt with survival data with cure fraction. In this article, we consider a class of semi-parametric transformation models, where an unknown transformation of the survival times with cure fraction is assumed to be linearly related to the covariates and the error distributions are parametrically specified by an extreme value distribution with unknown parameters. Estimators for the coefficients of covariates are obtained from pseudo Z-estimator procedures allowing censored observations. We show that the estimators are consistent and asymptotically normal. The bootstrap estimation of the variances of the estimators is also investigated. 2011-03-21T05:02:07.823Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12220 We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated. 2011-03-21T05:02:03.419Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12255 Sensitivity analysis, or so-called ‘stress-testing’, has long been part of the actuarial contribution to pricing, reserving and management of capital levels in both life and non-life assurance. Recent developments in the area of derivatives pricing have seen the application of adjoint methods to the calculation of option price sensitivities including the well-known ‘Greeks’ or partial derivatives of option prices with respect to model parameters. These methods have been the foundation for efficient and simple calculations of a vast number of sensitivities to model parameters in financial mathematics. This methodology has yet to be applied to actuarial problems in insurance or in pensions. In this paper we consider a model for a defined benefit pension scheme and use adjoint methods to illustrate the sensitivity of fund valuation results to key inputs such as mortality rates, interest rates and levels of salary rate inflation. The method of adjoints is illustrated in the paper and numerical results are presented. Efficient calculation of the sensitivity of key valuation results to model inputs is useful information for practising actuaries as it provides guidance as to the relative ultimate importance of various judgments made in the formation of a liability valuation basis. 2011-03-21T05:00:32.467Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:12023 As the actuarial profession in North America moves towards recognition of university studies for the purpose of professional qualification, it is timely to consider what may be learned from the Australian experience. Professional bodies have been accrediting Australian university actuarial programs since 1969. This paper examines the Australian actuarial qualification process from the perspective of what makes a good education system, and notes that there are a number of constraints imposed by the profession that impair the quality of students' learning outcomes. The paper goes on to suggest how these pitfalls might be avoided in the interests of providing future actuaries with an opportunity to develop the attributes they will need for their professional careers. 2011-03-02T07:11:13.540Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:11008 The estimation of loss reserves for incurred but not reported (IBNR) claims presents an important task for insurance companies to predict their liabilities. Recently, individual claim loss models have attracted a great deal of interest in the actuarial literature, which overcome some shortcomings of aggregated claim loss models. The dependence of the event times with the delays is a crucial issue for estimating the claim loss reserving. In this article, we propose to use semi-competing risks copula and semi-survival copula models to fit the dependence structure of the event times with delays in the individual claim loss model. A nonstandard two-step procedure is applied to our setting in which the associate parameter and one margin are estimated based on an ad hoc estimator of the other margin. The asymptotic properties of the estimators are established as well. A simulation study is carried out to evaluate the performance of the proposed methods. 2011-02-21T21:18:02.193Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:11729 In this paper, we develop an option valuation model in the context of a discrete-time multivariate Markov chain model using the Esscher transform. The multivariate Markov chain provides a flexible way to incorporate the dependency of the underlying asset price processes and price multi-state options written on several dependent underlying assets. In our model, the price of an individual asset can take finitely many values. The market described by our model is incomplete in general, hence there are more than one equivalent martingale pricing measures. We adopt conditional Esscher transform to determine an equivalent martingale measure for option valuation. We also document consequences for option prices of the dependency of the underlying asset prices described by the multivariate Markov chain model. 2011-02-18T15:30:37.463Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:11723 We consider a set of workers’ compensation insurance claim data where the aggregate number of losses (claims) reported to insurers are classified by year of occurrence of the event causing loss, the US state in which the loss event occurred and the occupation class of the insured workers to which the loss count relates. An exposure measure, equal to the total payroll of observed workers in each three-way classification, is also included in the dataset. Data are analysed across ten different states, 24 different occupation classes and seven separate observation years. A multiple linear regression model, with only predictors for main effects, could be estimated in 223+9+1+1 = 234 ways, theoretically more than 17 billion different possible models! In addition, one might expect that the number of claims recorded in each year in the same state and relating to the same occupation class, are positively correlated. Different modelling assumptions as to the nature of this correlation should also be considered. On the other hand it may reasonably be assumed that the number of losses reported from different states and from different occupation classes are independent. Our data can therefore be modelled using the statistical techniques applicable to panel data and we work with generalised estimating equations (GEE) in the paper. For model selection, Pan (2001) suggested the use of an alternative to the AIC, namely the quasi-likelihood under independence model criterion (QIC), for model comparison. This paper develops and applies a Gibbs sampling algorithm for efficiently locating, out of the more than 17 billion possible models that could be considered for the analysis, that model with the optimal (least) QIC value. The technique is illustrated using both a simulation study and using workers’ compensation insurance claim data. 2011-02-09T13:10:29.093Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10688 We develop a new exact filter when a hidden Markov chain influences both the sizes and times of a marked point process. An example would be an insurance claims process, where we assume that both the stochastic intensity of the claim arrivals and the distribution of the claim sizes depend on the states of an economy. We also develop the robust filter-based and smoother-based EM algorithms for the on-line recursive estimates of the unknown parameters in the Markov-modulated random measure. Our development is in the framework of modern theory of stochastic processes. 2011-02-07T01:21:47.746Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10399 The Administrative Appeal Tribunal’s decision in VBN v Australian Prudential Regulation Authority focused on decisions made by the corporate trustee of the AXA Australia Staff Superannuation Plan and by extension its directors. The AAT set aside disqualification orders made by APRA against seven of these directors pursuant to the Superannuation Industry Supervision Act 1993 (Cth). This decision is of value in its consideration of the extent to which superannuation (and other) trustees – and in turn those who may be made liable for its conduct – can be held legally accountable for (frequently difficult) decisions made in the management of a fund’s affairs. Issues considered include non-disclosure of relevant information to members, lack of due care and skill, and partial decision-making as between classes of members. The decision also considers in some detail the principles to be observed by an appellate tribunal or court in conducting a merits review of a trustee’s exercise of discretion. 2011-01-27T22:41:57.062Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10806 We study a portfolio selection problem in a continuous-time Markovian regimeswitching model. The market in this model is, in general, incomplete. We adopt a method to complete the market based on an enlargement of the market using a set of geometric Markovian jump securities. We solve the portfolio selection problem in the enlarged market for a power utility and a logarithmic utility. Closed-form solutions for the optimal portfolio strategies and the value functions are obtained in both cases. We also establish the relationship between the optimal portfolio problems in the enlarged market and the original market. 2010-11-30T09:10:28.510Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10810 9 page(s) 2010-11-30T09:10:15.151Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10811 In this article, we shall explore the state of art of stochastic flows to derive an exponential affine form of the bond price when the short rate process is governed by a Markovian regime-switching jump-diffusion version of the Vasicek model. We provide the flexibility that the market parameters, including the mean-reversion level, the volatility rate and the intensity of the jump component switch over time according to a continuous-time, finite-state Markov chain. The states of the chain may be interpreted as different states of an economy or different stages of a business cycle. We shall provide a representation for the exponential affine form of the bond price in terms of fundamental matrix solutions of linear matrix differential equations. 2010-11-30T09:10:14.739Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10812 We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes. 2010-11-30T09:10:07.387Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10736 In 2009, in the aftermath of the Global Financial Crisis, 140 American banks failed–and hundreds of other banks were classified as “problem institutions” by the FDIC. This has led to numerous books and articles examining the causes of systemic risk in our financial system. In this paper we step back in history, to see what we should have learned from a previous banking crisis, which occurred during the 1980s. In particular, we examine the downfall of the Penn Square Bank in 1982. The failure of the small Oklahoma bank caused enormous losses and widespread instability in the banking system. It is evident that many of the factors which led to the downfall of Penn Square in the 1980s have reappeared more recently–albeit in a slightly different guise. 2010-11-26T12:41:19.230Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:10743 We consider a risk minimization problem in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, observable and finite-state Markov chain whose states represent different market regimes. We adopt a particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a measure of risk. The risk-minimization problem is formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. One important feature of our model is to allow the flexibility of controlling both the diffusion process representing the financial risk and the Markov chain representing macro-economic risk. This is novel and interesting from both the perspectives of stochastic differential game and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided and some particular cases are discussed. 2010-11-26T12:41:06.866Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9767 We investigate, using questionnaires, the use of spreadsheet software in the financial sector workplace by recent graduates and the benefits of spreadsheets in the teaching and learning of actuarial and financial mathematics at postgraduate level. This study investigates the nexus between learning and work in order to modify the university curriculum. We aim to equip graduates with skills applicable in the workplace and to improve the learning of actuarial and financial theory. The results indicate that the use of spreadsheets in the workplace is ubiquitous and that graduates find them relatively easy to learn, easy to use and very useful for their work. Spreadsheet skills are considered very valuable. Little or no formal training had been provided during their university studies and graduates mostly learned on the job. The surveys of postgraduate students and of employers support the conclusions reached from the graduates’ survey. There is considerable justification for university courses to include training in the use of spreadsheets. 2010-10-19T01:21:54.855Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8694 This paper is particularly concerned with mean reversion in investment markets and its implications for investment market regulation. It is now well established that equity markets reflect a varying risk premium. It also seems that they and other investment markets are not necessarily always efficient and can sometimes move to extreme levels. Investors who rely on fundamental analysis of individual assets and asset classes can profit from such movements. Uninformed investors, on the other hand, can not only lose money by inadequate diversification and excessive trading, but also by being panicked into buying overpriced or selling under priced assets. This leads on to a consideration of other errors, identified by recent research, to which uninformed investors may be prone. Most important would appear to be the failure of superannuation members to adapt their investment strategy over their lifetimes. It is suggested that official and industry regulators should take behavioural finance insights into account in enforcing disclosure, and by encouraging a more thorough approach to the monitoring of investment performance. The pressure on uninformed and nervous investors to panic might be reduced by the publication of a consensus portfolio to act as a benchmark. 2010-09-08T04:51:12.160Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9383 This paper outlines the weaknesses in insurance regulation and supervision, which led to the failure of the Guarantee Security Life Insurance Company in Florida in 1991. There are comparisons to more recent failures of financial institutions in Australia, including Goldfields Medical Fund and Commercial Nominees. 2010-09-08T04:50:33.362Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9354 A critical problem in financial and insurance risk analysis is the calculation of risk margins. When there are a number of risks, the total risk margin is often reduced to reflect diversification. How large should the 'diversification benefit' be? And how should the benefit be allocated to the individual risks? We propose a simple statistical solution. While providing a theoretical analysis, the final expressions are readily implemented in practice. 2010-09-03T11:30:17.090Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9141 We Propose a Model for Valuing Participating Life Insurance Products under a Generalized jump-diffusion Model with a Markov-switching Compensator. It also Nests a Number of Important and Popular Models in Finance, Including the Classes of jump-diffusion Models and Markovian regime-switching Models. The Esscher Transform is Employed to Determine an Equivalent Martingale Measure. Simulation Experiments are Conducted to Illustrate the Practical Implementation of the Model and to Highlight some Features that can be Obtained from our Model. 2010-08-09T09:00:21.998Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8997 We investigate the use of spreadsheet tools, such as Microsoft Excel® in the workplace by recent graduates and the use of spreadsheets in the teaching and learning of finance theory and financial mathematics. We seek the opinions of recent graduates, employers and students using questionnaires. This study is conducted by the Department of Actuarial Studies in the Division of Economics and Financial Studies at Macquarie University, Australia. This study investigates: • The use of spreadsheets and other financial software in the workplace by recent graduates and the extent to which these skills were learnt at university or on the job, • The type of software skills required by employers of recent graduates, • The opinions and attitudes of postgraduate coursework students regarding the use of spreadsheets and financial software in the teaching and learning of actuarial and financial mathematics. In industrial practice, many complex and tedious financial and statistical calculations are done using spreadsheets. Spreadsheets can be used both to perform the calculations and to produce reports, tables and graphs to present the results. However, at university level the traditional approach used in teaching financial and actuarial mathematics is to get students to solve the problem using pen and paper and then to do all any calculations using a calculator. The traditional approach may be a barrier to the learning of financial theory for many students. This study investigates the nexus between learning and work in order to modify the university curriculum. We aim to equip graduates with applicable skills for use in the workplace and to improve the learning of financial theory. 2010-07-25T08:40:33.583Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:9000 NaN page(s) 2010-07-25T08:40:25.667Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8816 This chapter is concerned with distortion premium principles and some related topics. Apart from the characterization of a distortion premium principle, this chapter also examines the additivities involved in premium pricing and reveals the relationship among the three types of additivities. Furthermore, reduction of distortion premium to standard deviation principle for certain distribution families is investigated. In addition, ordering problem for real-valued risks (beyond the nonnegative risks) is addressed, which suggests that it is more reasonable to order risks in the dual theory than the original theory. 2010-07-02T07:21:37.249Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8688 We investigate the problem of scheduling n jobs on a single machine with the following features. The cost functions are general stochastic processes, which can be used to model the effects of stochastic price fluctuations, stochastic due times, etc., and the stochastic processing times follow a class of distributions, which includes exponential, geometric, and other families of distributions. Such a class of distributions is characterized by its characteristic functions. The optimal policies for these scheduling problems, both without precedence constraints, or with precedence in the form of nonpreemptive chains, are discussed, respectively. 2010-06-21T10:11:50.058Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8689 We study the problem of scheduling a set of jobs on a single machine, to minimize the maximum lateness ML or the maximum weighted lateness MWL under stochastic order. The processing time P i, the due date D i, and the weight W i of each job i may all be random variables. We obtain the optimal sequences in the following situations: (i) For ML, the {P i} can be likelihood-ratio ordered, the {D i} can be hazard-rate ordered, and the orders are agreeable; (ii) For MWL, {D i} are exponentially distributed, {P i} and {W i} can be likelihood-ratio ordered and the orders are agreeable with the rates of {D i}; and (iii) For ML, P i and D i are exponentially distributed with rates μ i and ν i, respectively, and the sequence {ν i(ν i+μ i)} has the same order as {ν i(ν i + μ i + A ₀)} for some sufficiently large A ₀. Some related results are also discussed. 2010-06-21T10:11:48.112Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8691 It is suggested that South African retirement schemes ought to be designed around the financial life cycle and the risks faced by the families of members at various stages of the cycle. This paper reviews what we know about the life cycle and the non-investment risks: principally death, disability, dismissal and divorce. Providing for death and disability within schemes would allow for an offset of these costs against that of retirement, for less in the way of underwriting and for economies of scope. It would also allow for the elimination of those statutory and private schemes that give partial cover for accidental causes of death and disability. The paper also criticises insurance arrangements that conflate the heterogeneous causes of disability. It then considers arguments for making scheme membership and various elements of design a legislative requirement. Against the common view, it is suggested that a relatively low level of saving should be required, but that life and disability cover ought to be compulsory as should annuitisation at retirement. 2010-06-21T10:11:42.740Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8692 8 page(s) 2010-06-21T10:11:39.867Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8629 Strategy prepares for effective operations. It seeks in particular to develop an organization’s market position and core competencies. These can also be described as intellectual capital, and can be effectively measured by actuarial values or forecasting techniques. Strategic risk is defined in this paper as a by-product of strategy, and can also be evaluated using appraisal values or the modelling of future scenarios. The paper then discusses the use of scenario planning, Delphi techniques and real option analysis to assist in the development of comprehensive strategic plans and the risks that threaten their successful implementation. 2010-06-17T09:00:41.998Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:1596 "To a teacher of an applied mathematics subject this makes heart-warming reading. If only all students could share the insights of this student! Perhaps that would be expecting too much. Nevertheless, it is both reassuring and inspiring to know that many students can and do experience the excitement, confidence and satisfaction that come with that kind of understanding”. This paper outlines the development of the course unit ACST201 over the period 1999-2001. The development was an attempt to implement several basic teaching principles within that unit. The reflection quoted above is regarded as one small indicator of the success of the development. 2010-06-17T07:10:07.139Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:8361 Context.The overshooting convective motions in the solar photosphere, resulting in the foot point motion of different magnetic structures in the solar atmosphere, are frequently proposed as the source for the excitation of Alfvén waves, which are assumed to propagate towards the chromosphere and corona resulting finally in the heating of these layers by the dissipation of this wave energy. However, the photosphere is a) very weakly ionized, and, b) the dynamics of the plasma particles in this region is heavily influenced by the plasma-neutral collisions. Aims.The purpose of this work is to check the consequences of these two facts on the above scenario and their effects on the electromagnetic waves. Methods.Standard plasma theory is used and the wave physics of the weakly ionized photosphere is discussed. The magnetization and the collision frequencies of the plasma constituents are quantitatively examined. Results.It is shown that the ions and electrons in the photosphere are both un-magnetized; their collision frequency with neutrals is much larger than the gyro-frequency. This implies that eventual Alfvén-type electromagnetic perturbations must involve the neutrals as well. This has the following consequences: i) in the presence of perturbations, the whole fluid (plasma + neutrals) moves; ii) the Alfvén velocity includes the total (plasma + neutrals) density and is thus considerably smaller compared to the collision-less case; iii) the perturbed velocity of a unit volume, which now includes both plasma and neutrals, becomes much smaller compared to the ideal (collision-less) case; and iv) the corresponding wave energy flux for the given parameters becomes much smaller compared to the ideal case. Conclusions.The wave energy flux through the photosphere becomes orders of magnitude smaller, compared to the ideal case, when the effects of partial ionization and collisions are consistently taken into account. 2010-05-27T07:10:12.732Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7892 We consider the problem of estimating the outstanding claims produced by a homogeneous general insurance portfolio. The specific model considered in this paper is one where the number of claims in any loss period follows a Poisson distribution, settlement delays follow the same multinomial distribution, and settlements are single lump sums that are independent identically distributed random variables. Simulations using this model reveal that the development ratios and the outstanding claims estimates produced using the chain ladder method are positively biased. We obtain approximate formulas for the biases using Taylor series expansions of the random variables about their means. The same methods ale used to obtain approximations for the variances and covariances of the projection ratios and the outstanding claims estimates. A simulation study reveals that OUI formulas ale highly accurate. 2010-04-22T08:40:07.365Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:4464 Practical and rigorous, this book treats GLMs, covers all standard exponential family distributions, extends the methodology to correlated data structures and discusses other techniques of interest and how they contrast with GLMs. The focus is on issues that are specific to insurance data and all techniques are illustrated on data sets relevant to insurance. Exercises and data-based practicals help readers to consolidate their skills, with solutions and data sets on the companion website. Although the book is package-independent, SAS code and output examples feature in an appendix and on the website. 2010-04-22T07:31:03.998Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7842 This is the first report to be released by the Institute's new Life Risk Insurance Committee and covers the investigation of Lump Sum business, including Death, TPD and Trauma experience and Immediate Annuities. It covers the two year period from 1/1/1998 to 31/12/1999. Whilst data volumes and quality has made the drawing of credible conclusions about trends and rates difficult there are indications that there is a need to review the standard tables used for solvency calculations. A new format of investigation is in development to allow better reporting and analysis of experience including the interaction between Death, IPD and Trauma cover to allow for better calculations of actual vs expected experience. The report also highlights the significant degree of variance in results between companies and the need to have full participation in the investigation if it is to produce credible and reliable results. 2010-04-21T09:41:04.428Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7793 This study of the causes of death among Australian insured lives over the period 1995-1999 is based on data collected by the Institute of Actuaries of Australia as part of its Personal Business Insured Lives Mortality Investigation. A comparison against population experience reveals low insured lives mortality for external causes of death (motor vehicle accidents, suicide and other external causes), cerebrovascular disease, digestive diseases and AIDS. It is clear from the analysis that both male and female insured cancer mortality relative to the population is substantially heavier in 1995-1999 than it was in 1990-1994, though the actual reason for the change cannot be determined with certainty. There is also the suggestion of a relative worsening in insured male suicide. As expected, there is evidence of selection effects for the non-external causes of death, and of high mortality among policies in the minimum evidence underwriting category. An unexpected finding is that medically underwritten policies experience the same or even slightly heavier mortality than non-medically underwritten policies; however it is possible that these groups have different underlying mortality prior to the underwriting process. Overall female insured mortality is 69% of that for males - identical to the result for 1990-1994 - with relatively light experience for the external causes of death and ischaemic heart disease, and relatively heavy experience for other neoplasms (which includes breast cancer). 2010-04-16T06:40:18.705Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7783 We examine the Laplace transform of the distribution of the shot noise process using the martingale. Applying the piecewise deterministic Markov processes theory and using the relationship between the shot noise process and the accumulated/discounted aggregate claims process, the Laplace transform of the distribution of the accumulated aggregate claims is obtained. Assuming that the claim arrival process follows the Poisson process and claim sizes are assumed to be exponential and mixture of exponential, we derive the explicit expressions of the actuarial net premiums and variances of the discounted aggregate claims, which are the annuities paid continuously. Numerical examples are also provided based on them. 2010-04-16T04:40:35.134Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:7788 The Lee-Carter (LC) method of mortality forecasting is well known and widely used. Two recent variants are the Lee-Miller (LM) variant and the Booth-Maindonald-Smith (BMS) variant. Both aim to improve the performance of the method. These two variants and the original Lee-Carter method are evaluated using data for twenty populations for 1900-2001, with the fitting period ending in 1985 and the forecast period beginning in 1986. Forecast errors are compared and decomposed, and uncertainty is examined. For these short-term forecasts, the two variants are generally more accurate than the LC method with narrower prediction intervals; and BMS marginally outperforms LM on these criteria overall. Further evaluation using different fitting periods is required. 2010-04-16T04:40:18.995Z ]]> http://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:3507 A new method for analysing and projecting mortality is proposed and examined. The method takes observed time series of survival probabilities, finds the corresponding z-scores in the standard normal distribution and forecasts the z-scores. The z-scores appear to follow a common simple linear progression in time and hence forecasting is straightforward. Analysis on the z-score scale offers useful insights into the way mortality evolves over time. The method and extensions are applied to Australian female mortality data to derive projections to the year 2100 in both survival probabilities and expectations of life. 2010-04-15T00:03:16.113Z ]]>