The Optimal Reinsurance In Stochastic Order

Comparing risk is an important role in the insurance practice and theory of the actuarial science. In the stochastic order sense, we have conducted the research for the optimal reinsurance. If taking all the risks as a set, and given some kinds of relations in the set, we derive some conception of the orders, thus make optimal decisions. In the stochastic order sense, we research the optimality on reinsurance and got some desired results.The content of the paper is divided into four chapters. In the first chapter we described the concept of reinsurance and its function, and some types of reinsurance and reinsurance market, and the policy in China; In the second chapter, by introducing the stochastic orders in probability theory, we studied the optimal reinsurance and derived the optimal deductible allocations of the excess-of-loss reinsurance in the stochastic order; In the third chapter, we studied the optimal reinsurance on mean-variance principle. For the insurer's benefit, we proved that the stop-loss reinsurance is the optimal insurance, so we got the optimal reinsurance on variance premium principle. In the forth chapter we stated the comparison of stop-loss reinsurance premium about dependent risks. We mainly discussed the premium comparison of stop-loss reinsurance in the individual risk models. Finally, the conclusions are made for the paper.