Class Of Compound Poisson-geometric Risk Model

Risk theory is a hot topic in the present actuarial science and mathematics research. It helps to construct the risk model in the light of the instrument of stochastic processes and to study the problem of adjustment coefficient and ruin probability. To make models more close to the actual operation of insurance company, we promote several risk models using probability,stochastic processes and martingale theory from the basic theory of bankruptcy, which enrich the study of insurance theory.Basing on the good nature of Poisson-Geometric process, the study of compound Poisson-Geometric risk model is increasing. Under this condition, we consider the proportional reinsurance and the excess reinsurance risk models, in which premium collection process is compound Poisson process, claim arrival process is compound Poisson-Geometric process, and interference term is random. We get the upper and lower bounds of adjusting coefficient and the expressions of bankruptcy probability using martingale theory in two cases.Finally, we further consider the proportional reinsurance and the excess reinsurance risk models with the investment return and inflation, and get the upper and lower bounds of adjusting coefficient and the expressions of bankruptcy probability.