Advance Research Of Generalized Poisson Risk Model

Martingale theory is a advancing theory of random process, the Martingale theory method has became a strong research tool,and goes forward to the other mathematics branch. The Martingale theory combining other mathematics branches has increasingly came to be some new research branches. In this paper the risk model of generalized Poisson distribution and other related question is discussed, and some related consequences are acquired.We introduce the classical risk model, and suppose that the premium process is a time linear function, using the diffusion approximation to compute the finite time ruin probability of this risk model, and using Martingale theory to estimate the upper bound for the ruin probability. Meanwhile we discuss the final ruin probability of the risk model of the insurance policy income with Poisson distribution, general Poisson distribution, double-insurance Poisson distribution and multi- insurance generalized Poisson distribution. With the multiplicity of the market economy, the variety of interest rate and the expansion of business, and according to the actual background of the company, the interference factor was added in the model to analyze the uncertain factor of the company.A new concept-standard claim X 0 was introduced from the actual background. Due to the different insurance firms and different ages of a insurance firm, the value of X 0 is different. The value is decided by history data of the insurance agent combined with the scale of the insurance firm. So in the condition of generalized Poisson distribution with interference, the concept of standard claim is introduced again in this paper to set up new risk model which is more approximate to the current market background. The Martingale theory is used to deduce the risk model ruin probability expression: which is proved to comply with the ruin probability upper bound, and discuss the existence of adjustment coefficient R . The new model makes the ruin theory more perfect.