英文标题：
《Optimal Risk Allocation in Reinsurance Networks》
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作者：
Nicole B\\\"auerle, Alexander Glauner
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最新提交年份：
2017
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英文摘要：
In this paper we consider reinsurance or risk sharing from a macroeconomic point of view. Our aim is to find socially optimal reinsurance treaties. In our setting we assume that there are $n$ insurance companies each bearing a certain risk and one representative reinsurer. The optimization problem is to minimize the sum of all capital requirements of the insurers where we assume that all insurance companies use a form of Range-Value-at-Risk. We show that in case all insurers use Value-at-Risk and the reinsurer\'s premium principle satisfies monotonicity, then layer reinsurance treaties are socially optimal. For this result we do not need any dependence structure between the risks. In the general setting with Range-Value-at-Risk we obtain again the optimality of layer reinsurance treaties under further assumptions, in particular under the assumption that the individual risks are positively dependent through the stochastic ordering. At the end, we discuss the difference between socially optimal reinsurance treaties and individually optimal ones by looking at a number of special cases.
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中文摘要：
在本文中，我们从宏观经济的角度考虑再保险或风险分担。我们的目标是找到社会最优的再保险协议。在我们的背景下，我们假设有n$的保险公司，每个公司承担一定的风险，还有一个代表性再保险公司。优化问题是最小化保险公司的所有资本要求之和，我们假设所有保险公司都使用一种风险范围价值。我们证明，如果所有保险公司都使用风险价值，并且再保险人的保费原则满足单调性，那么分层再保险条约是社会最优的。对于这个结果，我们不需要风险之间的任何依赖结构。在风险范围值的一般情况下，我们在进一步的假设下，特别是在个人风险通过随机排序正相关的假设下，再次获得了分层再保险条约的最优性。最后，我们通过观察一些特殊情况，讨论了社会最优再保险条约和个人最优再保险条约之间的差异。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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