Asymptotics for the ruin probability in a proportional reinsurance risk model with dependent insurance and financial risks

This article studies the joint ruin problem for two insurance companies that divide claims in positive proportions (modeling an insurance and re-insurance company). The arrival times of claims are delayed by a common random time. Suppose that the two insurance companies are allowed to make risk-free and risky investments, and the price processes of the corresponding investment portfolios are exponentials of jump-diffusion processes with common jumps. Furthermore, assuming that the claim sizes and their corresponding investment return jump possess a dependence structure, this article establishes an asymptotic formula for the ruin probability.