边际赔偿函数和违约风险下的最优再保险
The Optimal Reinsurance under the Marginal Indemnification Function and the Default Risk
摘要: 本文考虑了再保险人的违约风险，首先运用失真风险度量和失真保费原理建立了含有违约风险的总风险模型。其次通过边际索赔(MIF)函数与分出函数之间的关系建立了与总风险模型等价的MIF再保险优化模型。然后对MIF再保险优化模型的求解得到最优的边际索赔(MIF)函数，进而得到最优的分出函数。最后应用该方法研究了在VaR风险度量和Wang’s保费原理下的最优分出函数。
Abstract: In this paper, we consider the default risk of reinsurer. Firstly, we use the distortion risk measure and distortion premium principle to establish the total risk model with default risk. Secondly, by the relationship between the Marginal Indemnification Function (MIF) and the ceded loss function, we build MIF reinsurance optimization model equivalent to total risk model. Then, the optimal MIF function is obtained by solving the MIF reinsurance optimization model. Furthermore, the optimal ceded loss function is obtained. Finally, we apply this method to study the optimal loss function by the VaR risk measure and Wang’s premium principle.
文章引用：杜军红, 吴黎军. 边际赔偿函数和违约风险下的最优再保险[J]. 统计学与应用, 2017, 6(2): 146-155. https://doi.org/10.12677/SA.2017.62017

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