Ruin Probability Of Several Classes Discrete Time Risk Models With Dependent Interest Rates

Ruin probability is one of the main goals of the risk theory.In order to reduce the risk of bankruptcy,the insurance company tend to invest in part or all the assets for risk investment or purchase reinsurance.Therefore,it has practical significance to study the risk models with investment and reinsurance.Based on the above considerations,this paper studies the discrete time model with dependent interest rate and investment,and the reinsurance model with dependent interest rate,in which the interest rate is Markov chain structure and AR(1)structure.Recursive method and martingale method are used to estimate the corresponding upper bound of ruin probability.The conclusions obtained in this paper supplement related results for the discrete time risk model.This thesis is divided into five chapters.Chapter 1.This chapter briefly introduces the present situation of risk theory at home and abroad,as well as the background and significance of this chapter.And then the classical continuous time and the fully discrete time risk model are introduced.Finally,the main conclusions of this chapter are presented.Chapter 2.The ruin probability of a discrete time risk model with interest rate of AR(1)structure is studied,venture capital is considered simultaneously in the model.The upper bounds are obtained by using renewal recursive technique and martingale method respectively,the corresponding minimum upper bound for ruin probability is also discussed.Chapter 3.Upper bound for ruin probabilities are studied in a discrete time risk model with interest rate of Markov chain structure.The investment are assumed to be a constant.The return process of a stock market and the net losses are assumed to have an AR(1)structure.The upper bounds were derived by renewal recursive technique and martingale method respectively.Chapter 4.Considering a class of discrete time reinsurance model,in order to get the integral equation of ruin probability in the general reinsurance form,the time between the occurrence of the claims,the claim payment and the interest rate are assumed to be the AR(1)structure with different parameter in this model.As an application,the integral equation for ruin probabilities of the proportional reinsurance and the stop-loss reinsurance is obtained.Finally,the estimate of upper bound for ruin probability of proportional reinsurance is derived by renewal recursive technique.Chapter 5.Considering a class of discrete time reinsurance model.The claims and the time between the occurrence of the claims are assumed to be the AR(1)structure,the inter-est rates follows a Markov chain structure with a denumerable state space.The risk model of proportional reinsurance is considered.The upper bounds for the ruin probability are derived both by renewal recursive technique and martingale method.