Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk models

Abstract

Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al. (2010), the price process of the investment portfolio is described as a geometric Levy process. We study the tail probability of the stochastic present value of future aggregate claims. When the clai m -size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al. (2010).