Study On The Ruin Problems Of Two Classes Of Discrete Time Risk Models With General Premiums

In the classical compound binomial risk model,it is usually assumed that the premium received per period is one for convenience.However,the assumption may be restrictive and sometimes far from reality.Recently,the models with a general premium rate c(c?N~+) have been investigated by researchers.In this paper we study two classes of discrete time risk models.The first one is a class of discrete time renewal risk model with general premium rate,and the second is a compound binomial model with dependence setting,in which the waiting time until the next claim depends on the previous claim size.The conclusions obtained in this paper supplement related results for the discrete time renewal risk model.This thesis is divided into four chapters.Chapter 1.This chapter introduces the research background about the risk theory,and makes summary of the related definitions,properties and propositions in the discrete time risk model with unit premium and the compound binomial risk model with dependent structure.Chapter 2.Section 1 gives the discrete time renewal risk model with general premium rate.In section 2,we obtain the probability generating function of expected discount penalty function.In section 3,the explicit expressions for ruin related quantities are derived including the recursive formula for the expected discounted penalty function and the analytic expression for the deficit at ruin.Chapter 3.We construct the risk model of the dependence with an arbitrary premium rate in section 1.In section 2,we describe the Lundberg equation and discuss the roots of the equation.In section 3,the probability generating function of the Gerber-Shiu expected discount penalty function is given.By inverting the probability generating function,the defective renewal equation of the expected discounted penalty function is obtained.Chapter 4.In section 1 we analyze the defective renewal equation of the Gerber-Shiu function with K_m family claim sizes and geometric thresholds.We discuss the explicit expression for the probability generating function of the time to ruin with geometrical claims in section 2.In section 3,we present the numerical simulation.