Research On Dependence Theory With Insurance Risk And Financial Risk

In recent years,the risk theory has been one of the hot topics in the study of Actuarial Mathematics and Applied Probability,in which the core problem is to study the ruin theory.Because the theory of bankruptcy has extensive application value in risk management,it has attracted wide attention of scholars both at home and abroad.With the study of the ruin theory deeply,more and more factors need to be considered in the course of research.In stochastic economic environment,such as stochastic interest rates,stochastic return on investment and etc,among which factors are interdependent.Factually,for obtaining more profit,insurance companies will invest in some of their assets.Therefore,the insurance companies are confronted with two kinds of risks in a stochastic economic environment,one is the traditional claim insurance policy portfolio,and the other is the risk investment,which leads to investment risk.Obviously,these two kinds of risks are not independent,but the impact of financial risk on the insurance company is much more serious.Accordingly,the research on the contingent risk model with insurance risk and financial risk has more practical significance.In the past,a large number of literatures have used stochastic processing,product theory and heavy tailed distribution theory to study the asymptotic equivalence formulas of ruin probabilities in the case of the insurance risk and financial risk are independent of each other.In this paper,based on the theory of the product of random variables,heavy tailed distribution and etc,we discuss the dependence of discrete time insurance risk and financial risk.The main research contents are as follows:Firstly,the tail probability of the product of dependent random variables is studied,which is the theoretical basis of the later research.Then,we apply the conclusions to the study of insurance risk.We consider the independent and identically distributed random vector of the insurance risk and financial risk to satisfy the generalized FGM distribution,and insurance risk belongs to the intersection between the Dominatedly varying tailed class and the Long tailed class,under some special conditions,some precise asymptotic equivalence formulas are obtained for finite-time and infinite-time ruin probabilities.In the above studies,the asymptotic equivalence formulas of ruin probability are deduced in the form of linear combination partially.The linear combination is composed of the insurance risk and the tail probability of the financial risk,which can reflect the influence of the financial risk on the insurance companies.The dependence theory with insurance risk and financial risk has been enriched and developed.