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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
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.

Keywords

Ruin probabilityBrownian motionMartingale Ornstein–Ohlebeck process
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 16 , Issue 1 , April 1986 , pp. 33 - 43
Copyright
Copyright © International Actuarial Association 1986

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