基于均值-方差模型和违约风险的最优再保险设计

本文以保险公司最终财富的均值-方差效用最大化为目标，研究了在违约风险下的最优再保险设计问题。本文使用广义均值-方差保费准则，并假设违约因子与保险公司的总损失独立。本文通过构造法证明了在上述设定下的最优再保险形式为变换损失形式或变换损失与违约因子乘积的对偶形式。进一步，当保费准则中的保费附加函数单调，并且违约因子服从伯努利分布时，证明了最优再保险策略为成数再保险策略。当选择保费准则为标准差准则和期望值准则时，分别推导出了保险公司最优分出比例的表达式，发现最优分出比例与保险公司需要承担的总损失和违约因子的期望、方差，以及均值-方差模型下的风险规避系数有关。最后，基于所得到的理论研究结果，本文通过数值方法定量地计算了最优分出比例、风险规避系数和履约概率之间的关系。

研究发现，随着保险公司的风险规避系数变大，最优再保险的分出比例也变大。这说明保险公司对风险越厌恶，越倾向于分出更多风险给再保险公司共同承担。同时，保险公司信念下的履约概率越大，最优再保险的分出比例也越大。这表明保险公司对再保险公司完全赔付越有信心，越倾向于分出更多风险给再保险公司。

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