Ruin probability for L関y risk process compounded by geometric Brownian motion

Abstract

In this paper, we assume that the surplus of an insurer follows a L暍y risk process and the insurer would invest its surplus in a risky asset, whose prices are modeled by a geometric Brownian motion. It is shown that the ruin probabilities (by a jump or by oscillation) of the resulting surplus process satisfy certain integro-differential equations.