Optimal Reinsurance With Stochastic Dominance And MS Constraints

This paper, mainly in view of the insurance company which has many different kinds of risk, discusses the optimal proportional reinsur-ance problem with different constraints for the proportional reinsurance contract.Under the stochastic dominance constraints, the optimal reinsur-ance problem with the second order stochastic dominance constraints is given. When all the losses are discrete distributed, the existence of the optimal solution of the retention ratio is investigated. Further, the optimal reinsurance problem with stochastic dominance constraints is simplified by the dual problem. Besides, the existence theorem is also given for the divided model.Under the mean-standard deviation (MS, for short) rule constraint, the original problem of the optimal proportional reinsurance is also a convex programming problem. First, the equations which the optimal solutions satisfy are obtained, and then, by KKT conditions in convex programming problem, we get the existence theorem of the optimal so-lution. In this case, the dual problem of the optimization problem is also presented.When the optimal proportional reinsurance problem with two con-straints:stochastic dominance and MS rule is studied, the existence the-orem of the optimal solution with double constraints is obtained. In the end, the conclusions and prospects are given.