Research On Collective Risk Model When Claims Obey Exponential Distribution

The paper studies collective risk model when claims obey exponential distribution:(l)About short-term collective risk model Firstly, introduces four methods of discussing short-term collective risk model and brings forward the method of probability generating function , gives two qualities of compound binomial distribution and compound negative binomial distribution — reactivity and decomposability; Secondly, gives the conclusions of the total claims when claims obey exponential distribution.(2) About long collective risk model Firstly, gives the ruin probability when claims obey mixed exponential distribution on classical poisson risk model and an approximation of the ruin probability;Secondly, construct a multitype insurance poisson risk model, gives differential function of ruin probability and the ruin probability when claims obey exponential distribution.