The Probability of Ruin in a Kind of Cox Risk Model with Variable Premium Rate

In this paper the probability of ruin is investigated under the influence of a premium rate which varies according to the intensity of claims, and the occurrence of claims is described by a Cox process in the considered risk model. The idea is originally enlightened by Jasiulewicz (2001). We make a slight modification on the model and a generalization on the intensity process. By a "backward differential argument" and the Markov property of the intensity process we strictly derive the integral equation satisfied by the probability of ruin. Further, we solve the equation when the intensity process is a homogeneous n-state Markov process by Laplace transforms. At the end of the paper, an example is given. Keywords: Cox Risk Model, Ruin Probability, Variable Premium Rate, Markov Property, Integral Equation, Laplace Transform