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

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.