Asymptotic results for ruin probability in a two-dimensional risk model with stochastic investment returns

Abstract

This paper considers a two-dimensional time-dependent risk model with stochastic investment returns. In the model, an insurer operates two lines of insurance businesses sharing a common claim number process and can invest its surplus into some risky assets. The claim number process is assumed to be a renewal counting process and the investment return is modeled by a geometric Lévy process. Furthermore, claim sizes of the two insurance businesses and their common inter-arrival times correspondingly follow a three-dimensional Sarmanov distribution. When claim sizes of the two lines of insurance businesses are heavy tailed, we establish some uniform asymptotic formulas for the ruin probability of the model over certain time horizon. Also, we show the accuracy of these asymptotic estimates for the ruin probability under the risk model by numerical studies.