Optimal Reinsurance with Expectile Under the Vajda Condition
Optimal Reinsurance with Expectile Under the Vajda Condition
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DOI：
10.21314/jor.2020.444
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
Yanhong Chen
中科院分区：
文献类型：
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作者：
Yanhong Chen
在本文中，我们重新审视最优再保险问题，通过最小化调整后的价值，保险公司的责任，其中包括风险保证金。风险边际是由期望值决定的。为了体现再保险保护保险人的精神，我们假设保险人的自留损失和再保险人支付的赔款比例都在增加。保费原则被假定为满足以下三个性质：律不变性，风险负载和凸序保持。我们表明，最佳的割让损失函数的形式，三个相互连接的线段。进一步，当再保险费是平移不变的或遵循期望值原则时，得到了最优再保险合同的简化形式。最后，当再保险费为期望值原则或王氏保费原则时，给出了最优再保险协议的显式表达式。
In this paper, we revisit optimal reinsurance problems by minimizing the adjusted value of the liability of an insurer, which encompasses a risk margin. The risk margin is determined by expectile. To reflect the spirit of reinsurance of protecting the insurer, we assume that both the insurer’s retained loss and the proportion paid by a reinsurer are increasing in indemnity. The premium principles are assumed to satisfy the following three properties: law invariance, risk loading and convex order preservation. We show that the optimal ceded loss functions take the form of three interconnected line segments. Further, if the reinsurance premium is translation invariant or follows the expected value principle, simplified forms of the optimal reinsurance treaties are obtained. Finally, when the reinsurance premium is assumed to be the expected value principle or Wang’s premium principle, the explicit expression for the optimal reinsurance treaty is also given.