随机占优和MS约束下的最优再保险

发布时间：2018-06-27 10:47

本文选题：随机占优准则 + MS准则　；参考：《南京师范大学》2013年硕士论文

【摘要】：本文主要针对具有多类不同风险的保险公司,对比例再保险合同,在不同的约束准则下探讨最优比例再保险策略的问题. 在随机占优约束下,首先给出了二阶随机占优的最优再保险问题,当损失是服从离散分布的随机变量时,得到了最优自留比例系数的解的存在性定理,并在此基础上得到了原问题的对偶问题,从而把原有的随机占优约束下的最优再保险问题进行了简化,最后对该模型进行分裂,同样得出最优解的存在性定理. 在均值标准差(简称MS)准则约束下,原最优比例再保险问题同样也是一个凸规划问题.首先得到最优解所满足的方程组,通过凸规划中Karush-Kuhn-Tucker(简写成KKT)条件得到了最优解的存在性定理.同样也可以得到优化问题的对偶问题. 最后,对随机占优和MS准则双重约束下的最优比例再保险问题做了探讨,并给出双重约束下解的存在性定理,并对论文未来的研究内容进行了总结和展望.
[Abstract]:In this paper, the optimal proportional reinsurance strategy is discussed under different constraint criteria for the insurance companies with many kinds of different risks and for the proportional reinsurance contracts. In this paper, we first give the optimal reinsurance problem of second order stochastic dominance under stochastic dominance constraints. When the loss is a random variable with discrete distribution, we obtain the existence theorem of the solution of the optimal self-retention ratio coefficient. On this basis, the dual problem of the original problem is obtained, which simplifies the original optimal reinsurance problem under stochastic dominant constraints. Finally, the existence theorem of the optimal solution is obtained by splitting the model. Under the criterion of mean standard deviation (MS), the original optimal proportional reinsurance problem is also a convex programming problem. First, the equations satisfied by the optimal solution are obtained, and the existence theorem of the optimal solution is obtained by Karush-Kuhn-Tucker (KKT) condition in convex programming. The dual problem of optimization problem can also be obtained. Finally, the optimal proportional reinsurance problem under the double constraints of stochastic dominance and MS criterion is discussed, and the existence theorem of solutions under double constraints is given, and the future research contents of this paper are summarized and prospected.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840.69

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