Ruin Probabilities for Markov-Modulated Jump-Diffusion Risk Model

Abstract

In order to describe the dependent structure in the jump-diffusion risk model in non-life insurance, a Markov-modulated model is considered in this paper. By introducing an external continuous-time Markov process, the classical jump-diffusion risk model is extended to a Markov dependent one, in which the inter-claim time, the claim amount, the premium rate and the volatility of the diffusion process are all regulated by the Markov process. In this case, we obtain a generalized Lundberg's fundamental equation and derive a system of integrodifferential equations of ruin probabilities for Markov-modulated jump-diffusion risk model, which can effectively measure a type of dependent risk.