Study Of The Bankruptcy Of The Types Of Risk Models

There are five chapters in this paper.In the first chapter,we summarize the risk theory and the main context of this paper.The second chapter is the basic knowledge of the paper.And the last three chapters are the main parts of the paper.In this paper,we discussed some problems of three special risk models by recursive method and Martingale method.In the third chapter,we discussed the continuous-time renewal risk model with interest,and its premium is a Negative binomial distribution process.This model is amelioration to the renewal risk model of Jun Cai, David C.M.Dickson.In Jun Cai,David C.M.Dickson model,The premium is a constant and continuous.But in real world,more and more companies receive their premium stochastic.So in this chapter,we assume the premium is a Negative binomial distribution process basing the renewal risk model of Jun Cai,David C.M.Dickson.First,we discussed the upper-bound of ruin probability by recursive method and martingale method.Then we analysis the deficit at ruin by recursive method.In the forth chapter,we discussed discrete-time interest risk model。Discrete-time risk model have more practice meanings than continuous-time risk model in the numerical calculation.The common discrete-time risk model is compound binomial risk model.Consider the effect of the interest,we take interest into the account.For example,Lijuan Sun and Lan Gu study the constant interest discrete-time risk model.In this chapter,the model is more general.we assume the interests is i.i.d random variables and get the ruin probability's upper-bound.Then we discussed the deficit at ruin and the surplus prior to ruin.In the fifth chapter,we study a risk process with positive and negative risk sums.The common negative risk sums process is life annuity insurance.A big life insurance company has life annuity insurance and personal accident insurance also.The later can be discripted by positive risk sums process.By recursive method and Martingale method,we derive the integral equation for the survival probability and obtain the exponential inequality for the ruin probability.