Moments Of Deficit Duration And Its Proportion In Compound Binomial Model

This paper discusses the moment calculation of deficit duration based on the compound binomial risk model.The first chapter is the introduction part.In this chapter,we introduce the research background and content of this paper,as well as the main structure of the paper.The second chapter introduces the model and its construction,and makes some reasonable assumptions,and defines the rth moment of the deficit duration and its proportion.The third chapter studies the calculation of the rth moment of deficit duration and its proportion in finite time T.We construct an operator and a linear transformation,under the condition of positive safety load,the deficit duration gradually converges to a positive integer as time T gradually tends to be infinite,and this conclusion is verified by numerical calculation.The fourth chapter introduces the dividend barrier b in the risk model,studies the convergence of the deficit duration and its proportion under the positive safety load condition when T is gradually infinite,and the conclusion is verified by numerical calculation.In Chapter 5,when the dividend barrier b exists,we discuss the solution method of the time proportion when the surplus is less than an integer value,so as to obtain some information of the stable distribution.And we provide a numerical example of this problem.The sixth chapter introduces reinsurance strategy to optimize the deficit duration and minimize the proportion of deficit duration under the existence of dividend barrier b.Numerical examples illustrate the effectiveness of the proposed method.The seventh chapter summarizes the idea and main content of this paper,and points out the shortcomings of the article and the direction of the next research.