Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/74870
72 Visitors
91 Hits
2 Downloads
- Title
- Jump diffusion processes and their applications in insurance and finance
- Related
- Insurance, mathematics and economics, Vol. 41, Issue 1, p.62-70
- DOI
- 10.1016/j.insmatheco.2006.09.006
- Publisher
- Elsevier
- Date
- 2007
- FoR/RFCD Code(s)
-
010400 Statistics
140200 Applied Economics
- Author/Creator
- Jang, Jiwook
- Description
- 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.
- Description
- 9 page(s)
- Subject Keyword
- 010400 Statistics
- Subject Keyword
- 140200 Applied Economics
- Subject Keyword
- jump diffusion processes
- Subject Keyword
- joint Laplace transform
- Subject Keyword
- aggregate accumulated claims
- Subject Keyword
- non-defaultable zero-coupon bond
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Actuarial Studies
- Identifier
- http://hdl.handle.net/1959.14/74870
- Identifier
- ISSN:0167-6687
- Identifier
- mq-rm-2007001507
- Language
- eng
- Reviewed
