The other is the optimal free claims in excess of loss insurance.

With both the insurer s benefit and the reinsurer s benefit under consideration and on the assumption that investment fund follows lognormal distribution,the reinsurance pricing question affected by investment gains is discussed,and the pricing formula is established for proportion reinsurance and excess-of-loss reinsurance.

Using this method ,this paper first analyzes the option property of excess-of-loss reinsurance,and evaluates it by option pricing technique,then in a dynamic game theory model with complete information analyzes the optimal strategies of both o-riginal insurer and reinsurer as well as the equilibrium result,thus.

Starting from systematic view,the paper integrates compensations that insuers will be up against with its return on investment and establishes linear forward-backward stochastic differential equations for proportional and excess-of-loss reinsurance premiums.

We study the insurer s adjustment coefficient as a function of retention levels for combinations of quota-share with excess of loss reinsurance in the Sparre Anderson model.

China\'s over-insurance system does not distinguish between the causes ofover-insurance and apply different legal effect ,but all according to the provisions ofArticle 40th of "Insurance Act" only the over part invalid, resulting in seriousloopholes in the over-insurance system of China, can not effectively guard againstmalicious behavior of over-insurance and the occurrence of moral hazard.

When analyzing over insurance,we must follow the basic concept of insurance law,start with the declaration of will of the parties,distinguish the different reasons of over insurance and make different regulations of them.