Relevant Risk Models With Claim Numbers Following Zero-inflated Poisson Process

Bankruptcy theory is one of the important theoretical foundations for the development of insurance industry.Therefore,it is of great practical significance to establish a risk model that conforms to insurance practice and to study the bankruptcy related issues of insurance companies.In this paper,the Zero-inflated Poisson distribution used as the number of claims to establish a relevant risk model,starting with the classic risk model,and gradually considering the influence of interference factors and interest rate factors in the model,then obtain the relevant conclusions.This paper is divided into four chapters:Chapter 1,This chapter makes a brief introduction to the research background and related research results of bankruptcy theory.Finally,the main contents of this paper are summarized.Chapter 2,This chapter discusses the general risk model of the Zero-inflated Poisson process for claims,The first section describes the definition and properties of Zero-inflated Poisson process;The second section introduces the basic structure of the model;The third section studies the integral equation that the penalty function when the bankruptcy occurs,and then obtains conclusion of the ruin probability;The fourth section gives the analytical expression of the ruin probability when the claim amount is exponential distribution.Chapter 3,This chapter studies the Zero-inflated Poisson risk model with stochastic premium income.The first section introduces the basic structure of the model and some preparation knowledge.In the second section,we give the ruin probability of the risk model by martingale method.The third section analyze the analytic expressions of the ruin probability when the premium income and the claim amount are subject to the exponential distribution are analyzed.Chapter 4,The chapter introduces the constant interest rate based on the second chapter.The first section gives the basic structure of the model.The second section obtains the integral equation satisfied by the penalty function at the time of ruin.Section three gives the analytical expression of the penalty function when the initial surplus is zero.