Asymptotic Approximation Of Sum-ruin Probability For A Bidimensional Heavy-tailed Risk Model Under Dependence Structure

In the insurance industry,risk theory is the theory of mathematical analysis of various risks,through the establishment of risk models,mathematical analysis of them to solve practical problems.In the study of risk theory,the majority of scholars have established a variety of risk models to describe the complex insurance financial business,so risk model has always been a hot topic in the financial insurance risk management.In addition,the frequent occurrence of major disasters in recent years has brought some large claims to insurance companies,and the distribution of these large claims is usually heavy tailed rather than light tailed.In order to reduce the loss caused by the major risk to the insurance company and enable the insurance company to operate normally,this paper is devoted to the study of the heavy tailed risk model and its ruin probability.And because of the diversity of insurance,bidimensional risk model is a typical representative of multi-dimensional risk model,and bidimensional heavy-tailed risk model is more widely concerned.Therefore,this paper mainly considers the asymptotic estimation of the twodimensional heavy-tailed risk model and sum-ruin probability.However,most of the risk models are studied under the independent condition of claim size,claim-inter-arrival time and claim-arrival process.But the independent condition is too ideal.This paper considers the two-dimensional heavy-tailed risk model under the dependent condition.The first two chapters mainly introduce the research background and explain the basic symbols,concepts and conventions involved in the paper.Firstly,the research background of this paper is introduced,and then the definition of the heavy-tailed distributions,the bidimensional renewal risk model and the ruin probability related to the bidimensional risk model are introduced.The third chapter mainly introduces the asymptotic estimation of sumruin probability for a bidimensional renewal risk model with common shock claim-arrival processes.Considering a bidimensional continuous time renewal risk model,when claim-arrival processes N1(t)and N2(t)satisfy the common shock dependence,and both two lines of claim sizes are assumed to be strongly subexponential,the uniformly asymptotic estimation for sum-ruin probability within finite time is established,and the obtained result extends the one in Cheng and Yu[14].The fourth chapter mainly introduces the asymptotic estimation of sumruin probability for a bidimensional renewal risk model with a constant interest force under the dependent structure.Considering a bidimensional renewal risk model with a constant interest force,in which the claim sizes from the same business line are dependent following a general dependence structure proposed in Ko and Tang[28]and each pair of inter-arrival times of the two kinds of insurance claims are arbitrarily dependent.In the presence of subexponential claim sizes,the corresponding asymptotic formula for the finite-time sum-ruin probability is established.