Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/77899
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- Title
- Approximating the bias and variance of chain ladder estimates under a compound poisson model
- Related
- Journal of actuarial practice, Vol. 11, p.147-167
- Publisher
- Absalom Press
- Date
- 2004
- FoR/RFCD Code(s)
-
010200 Applied Mathematics
150200 Banking, Finance and Investment
- Author/Creator
- Yogaranpan, Janagan
- Author/Creator
- Clarke, Sue
- Author/Creator
- Ferris, Shauna
- Author/Creator
- Pollard, John
- Description
- 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.
- Description
- 21 page(s)
- Subject Keyword
- 010200 Applied Mathematics
- Subject Keyword
- 150200 Banking, Finance and Investment
- Subject Keyword
- outstanding claims
- Subject Keyword
- reserving
- Subject Keyword
- stochastic run-off triangles
- Subject Keyword
- chain ladder moments
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Actuarial Studies
- Identifier
- http://hdl.handle.net/1959.14/77899
- Identifier
- ISSN:1064-6647
- Identifier
- mq-rm-2004021677
- Language
- eng
- Reviewed
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