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

Published online by Cambridge University Press:  29 August 2014

F. Abikhalil*
Affiliation:
Université Libre de Bruxelles
*
Université Libre de Bruxelles, École de Commerce en CEME, CP135, Av. F. D. Roosevelt, 1050 Bruxelles, Belgium.
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Abstract

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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.

Type
Articles
Copyright
Copyright © International Actuarial Association 1986

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