一般保费原则下的帕累托最优再保险策略的研究

发布时间：2018-05-11 23:39

  本文选题：最优再保险 + VaR准则　； 参考：《山东师范大学》2017年硕士论文

【摘要】：再保险是保险人为了分散风险,将其所承担的风险的一部分转移给再保险人的一种保险.特别是当保险人面临巨大风险时,通过再保险转移风险是非常有必要的.而再保险中最关键的问题是最优再保险,如何选择最优再保险形式就成为保险人迫切需要解决的问题.目前,已有大量的文献从保险人的角度或者从再保险人的角度研究最优再保险.而一份再保险合同涉及保险人和再保险人双方,并且他们两者之间具有冲突的利益关系.保险人认为最优的再保险合同,对于再保险人来说未必是最优的,甚至有时是难以接受的.因此,在这篇文章中,我们同时考虑保险人和再保险人双方的利益,在VaR准则下研究帕累托最优再保险策略,它可以由保险人和再保险人的VaR的凸组合的最小值决定.我们假设再保险保费原则满足风险附加和保止损序的性质,根据不同的分出损失函数,可以得到不同的最优再保险策略.当分出损失函数是单调不减的凸函数时,采用几何的方法来确定最优再保险的策略.为了进一步证明我们已得到的结果的适用性,在再保费原则为Dutch保费原则和Wang's保费原则下,分别给出了最优再保险策略下的最优参数.当分出损失函数是单调不减的凹函数时,求得期望值保费原则下的最优再保险策略和最优参数.
[Abstract]:Reinsurance is a kind of insurance that the insurer transfers part of the risk to the reinsurer in order to disperse the risk. Especially when the insurer is facing huge risk, it is necessary to transfer the risk through reinsurance. The most important problem in reinsurance is optimal reinsurance. How to choose the optimal reinsurance form is an urgent problem to be solved by the insurer. At present, a large number of literatures have studied optimal reinsurance from the perspective of insurers or reinsurers. A reinsurance contract involves both the insurer and the reinsurer, and they have conflicting interests. The insurer thinks that the optimal reinsurance contract is not necessarily optimal or sometimes unacceptable to the reinsurer. Therefore, in this paper, we consider the interests of both the insurer and the reinsurer at the same time, and study Pareto optimal reinsurance strategy under the VaR criterion, which can be determined by the minimum value of the convex combination of the VaR of the insurer and the reinsurer. We assume that the reinsurance premium principle satisfies the properties of risk addition and stop loss order, and according to different loss function, we can obtain different optimal reinsurance strategies. When the loss function is a monotone convex function, the geometric method is used to determine the optimal reinsurance strategy. In order to prove the applicability of the obtained results, the optimal parameters under the optimal reinsurance policy are given under the Dutch premium principle and the Wang's premium principle, respectively. When the loss function is a monotone concave function, the optimal reinsurance strategy and the optimal parameters are obtained under the expected premium principle.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F840.69
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本文编号：1876184