Extension To Time Surplus Risk Model

Risk theory is a hot topic in the present actuarial science and mathematics research.By using stochastic processes theory,the classical risk theory studies mainly the surplus process of single-insurance,ruin time,ruin probability and adjustment coefficient.With the scale of the business expanding incessantly and the types of insurance increasing,there are obvious limitations of the classical risk model.So,in order to describe the risk that insurance company being faced with,many people generalized the classic risk models.In insurance mathematics,ruin theory is the mainly contents of insurance risk theory,as can supply a very useful early-warning measure for the risk of the insurance company,it has important theoretical and practical significance for the insurance company.In this dissertation,we get some generalized risk model by extends the time surplus risk model in two compound Poisson,dividend barrier and multiple-insurance, and gives a thorough research to this model under the conditions of numerical calculus in insurance.The thesis includes five chaptersThe first chapter:Introduces the evolutional course and actuality of risk model, expounded the direction,content and significance of this thesis.The second chapter:Imports the classical risk model and gives a definition of the time surplus risk model.The third chapter:This paper was meant to study the time surplus risk model of the premium collecting and claims settlement,both of which are Poisson processes.It mainly discussed the character of the time surplus in this model and derived the formula of ruin probability in this case.Further,when the single premium and arrival time of claims size distribution is exponential,correspond function curve is obtained.The forth chapter:The risk model of time surplus under the constant dividend barrier strategy is discussed.It mainly discussed constant and completely discrete case are Markov property.In particular,when the claim size distribution is exponential,the exact solutions probability function is obtained.The fifth chapter:The time surplus risk model of multiple-insurance is considered, we gain ruin probability formula and Lundberg inequality,we also give a explicit expression forψ(0)in the special condition.