The Analysis Of Discrete Risk Model Based On Poisson Autoregressive Process

In actuarial science, discrete risk model is a important mathematical model and describes some policies of the total claim amount. The main advantage is that calculation comes simple and effective, and the practical application is very extensive, we assume each of insurance claims which are independent of each other only have certain dependency relationship in the insurance period. In this paper we construct the discrete time risk model with sparse operator based on the counting process, the poisson regression time series into the aggregate number of claims risk model. In this paper, the main content of the structure is as follows:In the second chapter, we introduce the definition of the sparse operator, and describe the definition and properties of the aggregate risk model of the poisson based on sparse operator AR(1), and gives the total loss distribution Sn momen-t generating function to verify stability of the claim number and claim amount sequences.In the third chapter, this paper introduces the definition and properties of the aggregate risk model poisson ARMA (1,1) based on the sparse operator and gives the moment generating function of the total loss distribution Sn.In the forth chapter, as for the particularity of its operating risk, the stabil-ity of the insurance company is required to safeguard the interests of the policy-holders. One of the indicators is ruin probability. In this paper, we use the ruin probability as the risk measurement of insurance company, the introduction of the model based on poisson risk moving average polymerization of surplus process, and thus prove the poisson ARMA(1,1) the adjustment coefficient of aggregate risk model, and then estimates the ruin probability.Finally, we have done the numerical experiments for the ruin probability related, and give the relationship of the coefficient p and parameter a.