asymptotic ruin probabilities in a dependent perturbed integrated risk process with application

The present paper investigates two types of perturbed integrated risk models to compute the asymptotic ruin probabilities‎: ‎(i) the risk model which is perturbed by log-return rate‎, ‎jump process‎, ‎and brownian motion process with dependent structure between the insurance risk and investment risk when the claim sizes are pairwise strong quasi-asymptotically independent‎. ‎for this model‎, ‎we assume that the heavy-tailed claim sizes and return jumps are caused by the systematic factors with an arbitrarily dependent structure; (ii) the risk model in which the underlying price process is a geometric brownian motion‎, ‎and the jump diffusion process is modeled by a dependent affine process when the claim sizes are asymptotically independent‎. ‎for both dependent models‎, ‎the asymptotic ruin probabilities are obtained using mathematical approaches‎. ‎moreover‎, ‎some numerical studies with monte carlo simulation using the farlie-gumbel-morgenstern copula as the joint distribution function of claim sizes and return jumps are provided to verify the performance of asymptotic results‎. ‎some of the results show that‎, ‎under the framework of regular variation with dependence structure‎, ‎the asymptotic finite-time ruin probability is insensitive to the claim sizes.