The Research Of Actuarial Variables On Modified Compound Poisson-geometric Risk Model

Combining the current financial and insurance industry practice,considering the reinvestment,random interference and collect premiums for the composite process.And taking into account the insurance and NCD are launched by insurance companies.New the compound Poisson-Geometric risk model of Mao Z C and so on is further popularized,to bring it closer to the actual business operations of insurance companies,and the actuarial variables of modified compound risk model is researched.The main research results of the full text are as follows:Firstly,the investment risk model with interference is defined in which the premium income follows a compound negative binomial distribution and the claim numbers follows a compound Poisson-Geometric process.Through analyzing the properties of the surplus process,the ultimate ruin probability and the Lundberg inequality formula of upper bound for ruin probability are obtained.And using the martingale method,the time when the surplus reaches a level firstly,its Laplace translation,its mean and k order central moments(k(28)2,3)are obtained.Secondly,the premium income is assumed to be compound Poisson process on the basis of the risk model in the third chapter.The modified compound Poisson-Geometric model of the survival probability,Gerber-Shiu discounted penalty function and duration of negative surplus are studied by using the method of total expectation formula,so it's integro-differential equations is deduced.Finally,bouns boundary is introduced on the basis of the risk model in the fourth chapter.Integral-differential equations with boundary conditions for the expectation,the moment generating function and n order moment of the discounted dividend payments until ruin are given by the method of total expectation formula and strong Markov property of the surplus process.