Research On Dual Delayed Renewal Model And Exponential Premium Risk Model

In the past twenty years,the occupation time is widely used in risk theory,which at-tracts more and more attentions in the actuarial calculation of the insurance.It controls the risk as a risk management tool,such as helping companies to decide whether or not continue to operate after the bankruptcy recovery and checking the assets operation of the insurance company;severals of studies have shown.On the one hand,it can measure the world at a lower level of earnings to analyze the solvency of an insurance company.On the other hand,it can measure the time in good operating condition of an insurance company,which helps the company to determine the appropriate dividend strategy.In addition,the charging of premium is also crucial to the operation of the insurance com-pany.In real life,the insurance's business can be described as a.system,in which the premium will make the surplus reducing.Therefore.it is of great theoretical value and pra.ctical significance to study the occupant,and the premium of risk model.This paper mainly uses the method of transformation to study the position of dual risk model,which transforms a dual risk model with exponential distribution claim into a Cramer-Lundberg model with an arbitrary claim distribution.Based on the relationship between the original model and the transformed modelthe Laplace transform of occupa-tion time of the original model is given.At last,the influence of risk aversion coefficient with index premium risk model on bankruptcy correlation is also given.The content of the thesis can be summarized as follows:In chapter 1.we introduce the background of the research.There arc four parts in chapter 2.In the first part.of chapter 2.the introduction of the risk model is given:In the second part,the negative Levy risk process,scale function and some related theories of volatility are introduced.In the third part,we establish the relationship of occupants between the original model and the new one.And then,using the transformed classical risk model,the joint Laplace transform occupation time of three mutex intervals before the bankruptcy is derived in the last part.In chapter 3.we give the principle of index premium and some basic theories.Then we dis-cuss the influence of risk aversion coefficicent under the prineiple findex premiuim.Fimally,we summarize the contents and consider how to improve the further research in the future.