The Preliminary Research Of Re-Insurance For The Thinning Process Under Constant Interest

In this paper, we discussed a risk with Re-Insurance for the Thinning Processunder Constant Interest. The structures and arrangements of the full text as follows:First chapter, introduction part, briefly introduced the development of thebackground of risk theory and risk model these years.The second chapter, introduce some basic knowledge which used in this paper.In the third chapter, The Ruin Probabilities for a Classic of Double CompositeRisk Model is studied. A risk model with double composite Poisson process wasstudied, in which the arrival of the claims is a-thinning process of the arrival of thepremium incomes, and reduced the risk of the insurance company with theproportional re-insurance. Meanwhile, the effects of the random interference on theruin probability of insurance company were analyzed.The general expression of theruin probability and an upper bound of the ruin probability were given. Lindberghequation of the ruin probability is provided by means of martingale method, and theexistence of adjustment coefficient was proved.In the forth chapter, the main topic is "The Preliminary Research of Re-Insurancefor the Thinning Process under Constant Interest". A Composite risks model with the-thinning process and re-insurance under constant interest were studied. A necessarycondition of the insurance company was given. Meanwhile, an upper bound of therisk model was given by means of martingale method.In the fifth chapter, the live probability of re-insurance for the thinning processunder constant interest is studied. We deduce the integral differential equation for liveprobability of this model in the infinite time, obtain the differential equation for liveprobability when premiums and claims are exponential distribution. Then we discuss the partial differential integral equation for live probability in the limited time.In the sixth chapter, the live probability of re-insurance for the thinning processunder constant interest with interference is studied. Through the improvement of therisk model which appeared in chapter five, we get a new model with a more strictconstraint. We deduce the integral differential equation for live probability of thismodel in the infinite time, and the partial differential integral equation for liveprobability in the limited time.