Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors

摘要

Ruin problems of continuous-time models with various dependence structures under risky investment are extensively studied in the literature. Those studies focus on dependence structures arising from insurance businesses themselves and pay few attentions to dependence between insurance risk and investment risk. This study considers a continuous-time Poisson risk model with insurance claims and investment return jumps shocked by common systematic risk factors. Systematic risk factors cause immediate jumps of investment returns but there are often random delays for insurers to settle incurred claims. The study further assumes that the arrival times of claims are delayed by a common random time to the ones of their corresponding investment return jumps. When claim sizes are heavy-tailed distributed, a uniform asymptotic estimate for ruin probabilities of the model is established and a numerical study is given to show the accuracy of the result. The result captures the effect of the dependence structures caused by systematic risk factors on the asymptotic behaviors of ruin probabilities and allows arbitrary dependence structures between claim sizes and their corresponding investment return jumps.