The stop-loss reinsurance as one way of reinsurance can make insurers obtain the highest expected effectiveness but the lowest risk variance.

Aiming at stop loss reinsurance, this paper derives optimal pricing model of reinsurance on the basis of total claim amount using mean-variance premium principle and utility theory.

The upper and lower bounds of S~((m)) in the sense of convex order were investigated,and the distribution function and stop-loss premium of the upper and lower bounds of S~((3)) were derived;meanwhile,the upper bounds for stochastic Annuities in the sense of convex order were obtained and the expectation of present value funct.

Besides, in terms of the aggregate difference of stop-loss premiums between two risks, the precision of such approximation is quantitatively characterized.

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.