The Ruin Probability With Constant Interest Force

In this dissertation we investigate the asymptotic behavior of the finite-time ruin probability with constant interest and the tail probability of sums of upper tail independent random variables. This dessertation consists of three chapters. As follows are main contents.In chapter one we give a preface. In this chapter on the one hand we introduce the development and significance of the risk theory, on the other hand we give the background and purpose of our reseach. Besides, some contents about classical risk theory and heavy-tailed distribution are given.In chapter two we investigate the finite-time ruin probability of a continuous time renewal model under constant interest force with heavy tails. Firstly, we change the constans c denoting the total premium accumulated up to time t in the model of Chen and Ng[7] into a nondecreasing and right-continuous stochastic process C(t). Secondly, we suppose the distribution of claim sizes belongs to L∩D. At last, under the assumption that the claims are pairwise negatively dependent we derive some simple asymtotic relations for the finite-time ruin probability and extend the ERV class which the claim sizes belong to in the model of Chen and Ng[7] to the L∩D.In chapter three we discuss the tail probability of sums of upper tail independent random variables. Let{X_k, 1≤k≤n} be n upper tail independent and identically distributed random variables with common distribution F belonging to L∩D.At last we getFrom this result we can see the upper tail independence don't affect the asymptotic behavior of tail probability of sums of random variables.