The Uniform Tail Asymptotics In The Renewal Risk Model With An Exponential Levy Process

In this paper we investigate the uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model with an exponential Levy process. Consider an insurer is allowed to invest in risky stock and risk free bond markets. The price process of the investment portfolio is described as a geometric Levy process. When the claims have extended regular variation distributions, we obtain the tail asymptotics which holds uniformly for the finite-time horizon by using the method of randomly weighted sums. The follows are the main contents.In chapter one we give a preface. In this chapter we introduce the ruin probability theory and the development of the risk theory. Besides, we give the purpose and the results of our research.In chapter two we give some theories about ruin probability. And some contents about heavy-tailed distribution are given.In chapter three we investigate the uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model with an exponential Levy process. We extent the claim size distribution of Tang[28] to the class ERV(-α,-β). Finally we obtain that holds uniformly.