The Asymptotic Analysis For Ruin Probabilities In Two Kinds Of Risk Models

In the risk theory,the heavy tailed distribution is generally used to describe the claims caused by major natural disasters,such as earthquakes,hurricanes,tsunamis and so on.The probability of such events is very small and difficult to predict,but in case of accident,it will cause huge economic losses to the insurance companies,so it has been widely applied by probability scholars in recent years.The research trend of the heavy tailed risk model is that various dependent structures are introduced in the model so as to make it more consistent with the practice of the insurance company.Therefore,this paper mainly studies the asymptotic form of the ruin probability in two kinds of heavy tailed risk models.The content of this article is divided into five chapters.The first chapter is the introduction part,firstly introduces the research background and significance,then some classes of heavytailed distributions,some interval dependence structure and dependence structure between claim and claim interval are summarized,and then introduced the continuous time and discrete time risk model.lastly,we describe the current research status and development trend of two kinds of risk models.The second chapter considers the uniform asymptotics of finite time ruin probability with non standard continuous renewal risk model in the risk model,we consider a great research value of the dependent structure ??size dependent,discussing the upper and lower bounds of finite time ruin probability.In particular,considered all the conditions in this chapter equipped with the size-dependence structure between claims and inter-arrive time we will get the asymptotic equivalence which is more simple.The third chapter discusses the asymptotics of ruin probability in discrete random risk model,assuming that the net loss and the stochastic discount factor respectively satisfy different dependence structure,net loss distribution and stochastic discount factor are subject to the dominatedly-varying-tailed distributions,under some limited condition,we obtain the asymptotics of random time ruin probability.In particular,the random time of ruin is a finite constant or infinity,which corresponds to the finite-time and infinite-time ruin probability.The fourth chapter gives an example to concretely describe the index of ruin probability,taking People's Insurance Company of China as an example for empirical analysis.The last chapter makes a summary of the main results of this paper,and finally,the next step of the research is prospected.