Distributions for the risk process with a stochastic return on investments

Abstract

In this paper, we consider a risk model with stochastic return on investments. We mainly discuss the ruin probability, the surplus distribution at the time of ruin and the supremum distribution of the surplus before ruin. We prove some properties for these distributions and derive the integro-differential equations satisfied by them. We present the relation between the ruin probability and the supremum distribution before ruin.