A Note On The Compound Poisson Risk Model

With the deepening of the economic globalization and integration,the rapid development of science and technology,the diversity of the financial products and the theoretical support from the financial fragility,people have no choice but to face the increasingly complex risks.Further,it is more severe for the special industry which operates pure risks–insurance industry to manage and control risks.Therefore,the risk theory was created.In the risk theory,the most classical model is the classical risk model,in which the number of claims obeys the Poisson distribution and the Poisson process.Based on that,the paper gives the probability distribution mixing Poisson counting process with Zero-Inflated Poisson counting process,which called Zero-Inflated Poisson-Poisson distribution(i.e.ZIP-P distribution).In this paper,with making the number of claims approximate to this distribution,we apply the distribution to the classical risk model.And then,the paper discusses the related short-term collective risk model and the related long-term collective risk model.Finally,this paper extends the classical risk model,and introduces the double compound ZIP-P risk model and the double-type insurance ZIP-P risk model.Especially,the value-at-risk measurement is introduced in the discussion of short-term collective risk model.