Compound Poisson Risk Model To Promote

In the classical insurance model, it is assumed that the insurancecompany's premium income is a constant at per unit time and S(t) =sum from i=1 to N(t)Y_iis a compound Poisson Process in surplus{R(t),t≥0}. But it is limited in the practicality. Applying the theory of stochastic point process and martingale method, the thesis generalizes the classical model in arrival processes of claims and premiums income process. It deals with several kinds of risk models.First, the generalized compound Poisson risk model when the number of premium income is a Poisson process. In the model the premium arrival process is a homogeneous Poisson process and the claim counting process is a generalized homogeneous Poisson process. The main results about the model are finite-time ruin probabilities and a Feller's expression of non-ruin probability.Secondly, the generalized double Poisson risk model. In the model both the premium arrival process and the claim counting processes are the generalized homogeneous Poisson processes. The main results are an upper bound and an expression of finite-time ruin probability.Third, the generalized double-type insurance Poisson risk model. In the model the generalized double-type insurance Poisson risk model is studied. That is, the claim counting processes of the two insurances are the generalized homogeneous Poisson processes. The thesis also studies the generalized single Poisson double-type insurance risk model, in which the premium arrival process of the insurance is a homogeneous Poisson process while the claim counting process of the two insurances is a generalized homogeneous Poisson process. Then, the thesis does some research on the situation in which the premium arrival processes of the two insurances are both homogeneous Poisson processes and the claim counting processes of the two are generalized homogeneous Poisson processes. Thus, the expression of ruin probability, an upper bound and a Feller's expression of non-ruin probability are achieved.Finally, the risk model of Markov adjustment expense rate in two states. In the model we mainly consider the condition under which both policies and claim number processes are controlled by Markov process. The main result is the expression of finite-time ruin probability.