The Study On Some Risk Models And Ruin Probability With Stochastic Premium And Disturbances Under Different Aspects

The classic compound Poisson risk model is a kind of basic model. But this kind of model could not be applied to practice well, so we get some generalized risk model by extending the classic risk model in some different aspects and do some reseaches on them. First, two one tpye-insyrance risk models are studied, which are A Class of Risk Model of Compound Poisson Process with Refund and The Risk Model Based on Related Arriving of Premium and Claim with Random Interest and Interference. Later on, A Double type-insurance Risk Model with Stochastic Premium is discussed and we will do some stochastic analyses on a discrete double type-insurance risk model. And some results about the ruin probability and its upper bounds are reseached. It mainly constants the following results(1) Considering refund event of insurance company, a new risk model, with the different Poisson flows of the arrival of the insurance policy, refund and claim, was introduced in this paper, which the premium, individual refund size and cliam size are i.i.d variables. Then we discussed the baisc property, ruin probability and its upper bound of the model mathematically. The relatives between adjust coefficient and model parameters also were analyszed numberically, which the adjust coefficient is a key to control the ruin probability. The results of the ruin probability characteristics provide some good ideas for insurance company to prevent some risks.(2) For a kind of asset insurance, under the condition of related arriving of premium and claim, a new risk model with random interest,interference and random premium was stablished, which the premium contained pure premium and other premium from part claim, in the same time the claim also contained two parts pure claim and other claim that could introduce some premium. A computation of ruin probability on this model was studied by martingale, then the comparision results about two special situations in this model and other two models was obtained.(3) A double type- insurance risk model was established in which the premium is a random variable, to study the adjustment coefficient and its relevant properties. Then, an upper bound for the ruin probability of this risk model is obtained by martingale. Finally, in one insurance type, we focus on analyzing the stochastic ordering relationship about total numbers of insurance policy at timet M₂₁(t)and total claim times at timet N₂₁(t). (4) We study a discrete-time renewal and double-type-insurance risk model, where in double insurance types, the occurrence of claims are two different renewal processes. We discuss via random walk an upper bound of the infinite-time ruin probability in this model. Then under the situation of exponential distribution, we compare this model with another model by discussing the relationship of adjustment coefficient in two models.