Bounds of Ruin Probability for Regime-switching Models Using Time Scale Separation

Abstract

This paper is concerned with regime-switching insurance risk models. The regime-switching is modeled by a continuous-time Markov chain. Owing to various modeling considerations, the state space is likely to be very large. A two-time-scale formulation is used to reduce the complexity. Under simple conditions, limits of ultimate survival probabilities and ultimate ruin probabilities are obtained. These results reveal that, for example, as a decision maker, one may ignore the detailed variations, and use the limit ultimate ruin probabilities to approximate that of the actual ones. Moreover, the differences of the original and limit ruin probabilities are examined. Error bounds are developed.