A Decomposition of the Ruin Probability for Risk Process with Vasicek Interest Rate

摘要

In this paper,it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market,and the interest structure of the bond market is assumed to follow the Vasicek interest model.This paper focuses on the studying of the ruin problems in the above compounded process.In this com- pounded risk model,ruin may be caused by a claim or oscillation.We decompose the ruin probability for the compounded risk process into two probabilities:the proba- bility that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived.When the claim sizes are exponentially distributed,the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.