Two Risk Models With Constant Interest Force And Dependence Structure

Large part of the surplus of the insurance companies comes from investment income,so more researchers on actuarial theory pay attention to deterministic interest rate.The theoretic basis of early work is independent increment property,but this condition may result larger deviation of risk evaluation.So considering dependence structure has great theoretical significance and applicable value in risk process.Consider two risk models with constant interest force and dependence structure.The first one is a class of renewal risk model with a good framework between the inter-claim and subsequent claim size,and obtain its upper and lower bounds for the tail distribution of the deficit at ruin and some problems about threshold dividend strategy.The second is a dependence structure with random threshold,and consider its upper and lower bounds for the tail distribution of the deficit at ruin and present numerical experiment to illustrate the validity of the model.This thesis is divided into three chapters.Chapter 1.As an introduction,this chapter first introduces the research background about the compound Possion risk model.Then it makes a brief summary of constant interest force,dependence structure and threshold dividend strategy and their research productions.Finally the main research work and significance of this paper are discussed.Chapter 2.This chapter discusses a class of renewal risk model with an exponentially weighted framework between the inter-claim and subsequent claim size.Section 1 gives the dependence risk model for details.Section 2 derives its upper bound for the tail distribution of the deficit at ruin by recursive techniques and upper and lower bounds in the case of life distributions.With threshold dividend strategy,section 3 obtains Gerber-Shiu expected discounted penalty function's integro-differential equation and expected discounted dividend function's integro-differential equation.Chapter 3.On the basis of chapter 2,this part constructs a dependence structure with random threshold.In section 1,it describes this risk model.In section 2,it discusses functional and exponential type upper and lower bounds for the tail distribution of the deficit at ruin.In section 3,numerical experiment is presented to prove constant interest force's effect on ultimate ruin probability when variables submit to exponential distributions.