| The insurance company which manage risk is different from otherfinancial industries. Usually the premium income is earlier than claimexpenses, and cash outflows are later than cash inflows. The occurrencetime and claim amount of insurance accident can not be determined inadvance. As the particularity of management,it needs the insurancecompany to keep its operating stable to protect the interests of the insured.And one measure of the stability of operating is ruin probability.Thestudy of ruin theory can not be separated from risk models.The classicalrisk model is one of the main risk models. However, the assumptions ofthe classical risk model are too idealized, and it is not fit for insurancereality. The classical discrete risk model assumes that the aggregate claimamount for different insurance portfolios are independent.However, theaggregate claim amount for different insurance portfolios are dependentin fact.In the discrete-time risk model based on thinning, this paper usemoving average time series to describe the behavior of the claim numberfor different insurance portfolios. The aggregate claim amount fordifferent insurance portfolios are dependence because of the temporaldependence relationship of the claim number sequence. First of all, take the second order poisson moving average riskmodel as an example, this paper introduces the definitions and propertiesof the poisson moving average risk model based on thinning, andgive the moment generating function of the aggregate claim amount overthe first n periods.Also it proves the stationary of the claim number seriesand the claim amount series. Secondly, it introduces Esscher premiumprinciple and its properties, and it also gives the Esscher premium of thefirst order poisson moving average risk model. Finally, it introduces somebasic knowledge of ruin theory,and gives the ruin probability and theadjustment coefficient of the first order poisson moving average riskmodel,and study the impact pf the parameter. |
