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Document Details : Title: Finite Time Ruin Problems for Perturbed Experience Rating and Connection with Discounting Risk Models Author(s): ABIKHALIL, F. Journal: ASTIN Bulletin Volume: 16 Issue: 1 Date: April 1986 Pages: 33-43 DOI: 10.2143/AST.16.1.2015015 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 rum 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. |
