Uniform Asymptotics Of The Ruin Probabilities In A N-dimensional Renewal Risk Model Under Strongly Subexponential Claim Sizes

The research on ruin probability is a significant branch of risk theory and ruin probability is a standard which measures the solvency of insurance company.The research has a profound impact on the practical operation.Many researchers have studied the uniform asymptotic results of ruin probability in renewal risk model and have come to a lot of meaningful conclusions.However,there are little research results about high dimensional renewal risk model and the uniform asymptotic results of ruin probability about the model.Generally,researchers focus on the large deviation results of ruin probability which are due to the claims from single type of insurance policy.This assumption is contrary to realism,so we devote to study the asymptotic results of ruin probability in a n-dimensional renewal risk model under strongly subexponential claim sizes in this paper.In this paper,we introduce and explain some related notations including renewal counting process,strongly subexponential class and surplus process firstly.Then,we specify the n-dimensional renewal risk model under strongly subexponential claim sizes and raise up necessary assumptions and useful lemmas in the second part of this paper.We present main results in the next part.Finally,we prove the main results,respectively.