Large deviations for the stochastic present value of aggregate claims in the renewal risk model

In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of aggregate claims. In this paper, the large deviations for the stochastic present value of aggregate claims, when the claim size distribution is of Pareto type with finite variance, are obtained.