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On the ruin probability of a generalized Cramér–Lundberg model driven by mixed Poisson processes

Part of: Applications Stochastic processes

Published online by Cambridge University Press:  12 September 2022

Masashi Tomita ,
Koichiro Takaoka  and
Motokazu Ishizaka Open the ORCID record for Motokazu Ishizaka [Opens in a new window]
Masashi Tomita*
Affiliation:
Meiji Yasuda Life Insurance Company
Koichiro Takaoka*
Affiliation:
Chuo University
Motokazu Ishizaka*
Affiliation:
Chuo University
*
*Postal address: 1-1, Marunouchi 2-chome, Chiyoda-ku, Tokyo 100-0005, Japan. Email: [email protected]
**Postal address: Faculty of Commerce, Chuo University, 742-1 Higashinakano, Hachioji-shi, Tokyo 192-0393, Japan.
***Email address: [email protected]
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Abstract

We propose a generalized Cramér–Lundberg model of the risk theory of non-life insurance and study its ruin probability. Our model is an extension of that of Dubey (1977) to the case of multiple insureds, where the counting process is a mixed Poisson process and the continuously varying premium rate is determined by a Bayesian rule on the number of claims. We use two proofs to show that, for each fixed value of the safety loading, the ruin probability is the same as that of the classical Cramér–Lundberg model and does not depend on either the distribution of the mixing variable of the driving mixed Poisson process or the number of claim contracts.

Keywords

Risk theoryvarying insurance premiumconditional distributionBayesian estimatoradjustment coefficient

MSC classification

Secondary: 60G44: Martingales with continuous parameter 62P05: Applications to actuarial sciences and financial mathematics
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 849 - 859
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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