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Finite Time Ruin Problems for Perturbed Experience Rating and Connection with Discounting Risk Models

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  • Abikhalil, F.

Abstract

We consider a generalisation of a risk process under experience rating when the aggregation of claims up to time t is a Brownian motion (B.M.) with a drift. We prove that the distribution of ruin before time t is equivalent to the distribution of the first passage time of B.M. for parabolic boundary. Using Wald identity for continuous time we give an explicit formula for this distribution. A connection is made with discounting risk model when the income process is a diffusion. When the aggregation of claims is a mixture of B.M. and compound Poisson process, we give (using Gerber's result 1973) an upper bound for the distribution of finite time ruin probability.

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  • Abikhalil, F., 1986. "Finite Time Ruin Problems for Perturbed Experience Rating and Connection with Discounting Risk Models," ASTIN Bulletin, Cambridge University Press, vol. 16(1), pages 33-43, April.
    • Handle: RePEc:cup:astinb:v:16:y:1986:i:01:p:33-43_00
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    Cited by:

    1. Powers, Michael R., 1995. "A theory of risk, return and solvency," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 101-118, October.
    2. Krzysztof Burnecki & Marek A. Teuerle & Aleksandra Wilkowska, 2022. "Diffusion Approximations of the Ruin Probability for the Insurer–Reinsurer Model Driven by a Renewal Process," Risks, MDPI, vol. 10(6), pages 1-16, June.

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