Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/138023
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- Title
- Nonparametric Bayesian credibility
- Related
- Australian actuarial journal, Vol. 15, Issue 2, (2009), p.209-230
- Related
- http://www.actuaries.asn.au/Library/AAJ_Vol15_Iss2_web.pdf
- Publisher
- Institute of Actuaries of Australia
- Date
- 2009
- FoR/RFCD Code(s)
-
010200 Applied Mathematics
150200 Banking, Finance and Investment
- Author/Creator
- Siu, T. K
- Author/Creator
- Yang, H
- Description
- 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.
- Description
- 22 page(s)
- Subject Keyword
- 010200 Applied Mathematics
- Subject Keyword
- 150200 Banking, Finance and Investment
- Subject Keyword
- nonparametric Bayesian credibility
- Subject Keyword
- risk characteristic of policyholder
- Subject Keyword
- random probability distribution
- Subject Keyword
- credibility premium principle
- Subject Keyword
- Dirichlet process
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Actuarial Studies
- Identifier
- http://hdl.handle.net/1959.14/138023
- Identifier
- ISSN:1442-3065
- Identifier
- mq-rm-2009002178
- Language
- eng
- Reviewed
