On The Ruin Problems For A Class Of Discrete Time Dependent Risk Model

This thesis studies a class of discrete time updating risk models with dependent structures,comparison between the claim amount and the random threshold,the risk process converts to each other in two levels.When the amount of the claim is less than the threshold,the risk process is changed.When the amount of the claim is greater than the threshold,the risk process does not change.To make the study convenient,it is assumed that the premium income per unit time is 1,it firstly obtains the analytical expression of the probability generating function satisfying the expected penalty function,and obtains the analytic solution of the zero initial value.Through the discussion of the root of the Lundberg basic equation,we further get the defect renewal equation satisfying the expected discount penalty function.This paper can be used as a supplement to the discrete time dependent risk model.This thesis is divided into four chapters.In chapter 1,the first section briefly introduces the important theoretical value of risk theory in practice and the recent research situation of dependent structural risk model;the second section introduces four kinds of concrete dependent structures;the third section makes a brief exposition of the research results.In chapter 2,the first section establishes the basic structure of the dependent risk model studied in this paper;the second section introduces the definition and properties of a class of discrete operators that need to be used in this paper;the third section obtains the probability generating function of the expected discounted penalty function.In chapter 3,the first section establishes the Lundberg equation of the model studied and discusses the root of the equation;the second section inverts the probability generating function of the expected penalty function;the third section obtains the defect update equation satisfied by the expected discount penalty function.In chapter 4,the first section gives some relevant conclusions when both the threshold value and the claim amount are geometric distribution;the second section draws the results of the numerical simulation.