The First Two Moments Of Ruin And Recovery Times In The Compound Binomial Model

The main aim of this paper is to study the first two moments of ruin and recovery times in the compound binomial model.The compound binomial model firstly proposed by Gerber(1988),which is a discrete-time version of the compound poisson model.We assume the insurance company continues if ruin occurs.Under the net profit condition,the surplus will be above zero in the future although the company is at risk. Furthermore, the process will go to infinity with probability one. Moreover, the times of ruin are finite. In this paper we mainly discuss the first two moments of the ruin time T, recovery time Ti (i = 1,2, ...N) and the sum of recovery time T in the compound binomial model by renewal method and martingale method when the initial surplurs is u.They depend on the distribution of severity of ruin.This paper includes six chapters. The first chapter is introduction. In the second chapter, the compound binomial model is introduced. In the third chapter,we mainly discuss the first two moments of the ruin time T, recovery time T_i and the sum of recovery time T in the compound binomial model by renewal method and martingale method when the initial surplurs is u.In the forth chapter ,we discuss the relation between the ruin time T and the first recovery time T₁ when the initial surplurs is u = 0. In the fifth chapter ,we give a example which the claim size distribution is independent and identical geometric distribution.The last chapter gives conclusions of this paper.