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.
