On The Discounted Penalty Function For The Compound Markov Binomial Risk Model With Delayed Claims

Classic binomial risk model is the discrete time renewal risk process which has been studied deeply in actuarial literature. However, the assumption of classic binomial risk model is too restrictive, and the existing problems in real life are seldom considered. Therefore, experts gradually generalize and supplement the classical risk model to make it more close to the reality. In this paper, we generalize the binomial risk model to compound Markov binomial risk model with delayed claims, and the main subject of the paper is the discounted penalty function.This thesis is divided into four chapters:The first chapter describes the compound binomial risk model and compound Poisson risk model, then the Markov process is reviewed. Finally, we give the definition of compound Markov binomial risk model and the meaning of our research.Chapter two first gives the structure of compound Markov binomial risk model and definition of the expected discounted penalty function. Starting from the definition, we give the relationship between the conditional penalty function with different initial value by using the claim time sequence {τ(n), n=1,2,…}.In the third chapter, by introducing an auxiliary process, we give the probability generating function m (s｜1) and m1(s｜1) of the conditional penalty m(u｜0) and m(u｜1) respectively.In the fourth chapter, we use a discrete operator to derive the renewal equation of the expected discounted penalty function. We first give the definition of discrete operator, then the numerator and denominator of m(s｜1) are expressed through the discrete operator, then the renewal equation of the expected discounted penalty function is obtained. As an application of the conclusions of the paper, we assume that the main claims and by-claims both follow geometric distributions, and then give the renewal equation of the expected discounted penalty function m(u｜1).