The Study Of Premium Pricing Model Under Compound Poisson Process With The Generalized FGM Dependence Structure

Premium pricing has always been the core issues of insurance theory and practice of the study. The business of insurance company can be described as an input-output system, in this system, the profit increased by the earned interest, collected premiums, and investment income, reduced by the expenses and cost of claims. Underpriced premiums will cause financial difficulties or even bankruptcy, overpriced premiums will reduce the competitiveness of the insurance companies in the market and increase the burden on the insured. Therefore, the premium pricing of insurance companies is a very important actuarial problem. The premium pricing is to calculate a minimum premium, which can not only meets the claims, but also makes the profit of protfolio grow fastly enough. The Determining of premiums is crucial to the survival of insurance company. Therefore, reasonable risk pricing model has been widely concerned by the insurance practitioners and theorists.This paper starts from the basic theories of insurance premium pricing, considers the claim and the waiting time be a sequence which has generalized FGM dependence structure. The premium pricing conducted in-depth exploration and research in the compound Poisson process model assumption, which is more practical relative to the independent case. After determining the distribution function of the compound Poisson process under the generalized FGM Copula, we derived expressions for the moment generating function of the claim amount by the method of Laplace transform, Laplace transform etc, and compared the moment generating function of independent claim amount and waiting time.Then this article discussed the calculation method of the high order derivatives of the moment generating function. We obtained the expression of Esscher pricing function, used the Matlab software to make the numerical simulation for the relation between the Esscher pricing function and the parameter h. We discussed the expressions of the premium with zero force of interest case and non-zero force of interest case.Finally, the article make a summary to the research results through the full text,and introduces the next step of the work plan.