Large deviations for the stochastic present value of aggregate net claims with infinite variance in the renewal risk model and its application in risk management

Abstract

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 present Levy process. People always are interested in estimating the tail distribution of the stochastic present value of aggregate claims. In this paper, the large deviation for the stochastic present value of aggregate net claims, when the net claim size distribution is of Pareto type with finite expectation are obtained. We conduct some simulations to check the accuracy of the result we obtained and consider a portfolio optimization problem that maximizes the expected terminal wealth of the insurer subject to a solvency constraint.