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

We consider a generalization 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. KEYWORDS ruin probability, Brownian motion, Martingale Ornstein-Ohlebeck process.