英文标题：
《An Optimal Multi-layer Reinsurance Policy under Conditional Tail
  Expectation》
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作者：
Amir T. Payandeh Najafabadi and Ali Panahi Bazaz
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最新提交年份：
2017
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英文摘要：
  A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer\'s total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy $f(\\cdot).$ In the first step, it cuts down an interval $[0,\\infty)$ into two intervals $[0,M_1)$ and $[M_1,\\infty).$ By shifting the origin of Cartesian coordinate system to $(M_{1},f(M_{1})),$ and showing that under the $CTE$ criteria $f(x)I_{[0, M_1)}(x)+(f(M_1)+f(x-M_1))I_{[M_1,\\infty)}(x)$ is, again, an optimal policy. This extension procedure can be repeated to obtain an optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal multi-layer reinsurance policy are estimated using some additional appropriate criteria. Three simulation-based studies have been conducted to demonstrate: ({\\bf 1}) The practical applications of our findings and ({\\bf 2}) How one may employ other appropriate criteria to estimate unknown parameters of an optimal multi-layer contract. The multi-layer reinsurance policy, similar to the original stop-loss reinsurance policy is optimal, in a same sense. Moreover it has some other optimal criteria which the original policy does not have. Under optimal criterion of minimizing general translative and monotone risk measure $\\rho(\\cdot)$ of {\\it either} the insurer\'s total risk {\\it or} both the insurer\'s and the reinsurer\'s total risks, this article (in its discussion) also extends a given optimal reinsurance contract $f(\\cdot)$ to a multi-layer and continuous reinsurance policy.
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中文摘要：
保险公司通常的再保险政策允许一层或两层付款扣除额。在最小化保险人总风险的条件尾部期望（CTE）风险测度的最优准则下，将最优止损再保险政策推广到最优多层再保险政策。为了实现这样的最优多层再保险政策，本文从给定的最优止损再保险政策$f（\\cdot）开始。$在第一步中，它将一个区间$[0，M\\u 1）$分为两个区间$[0，M\\u 1）$和$[M\\u 1，infty.$，通过将笛卡尔坐标系的原点移到$（M\\u 1}，f（M\\u 1}）），$，并显示在$CTE$标准下$[f（x）I\\u{[0，M\\u 1}（x）+（f（x-M\\u 1））I{[M\\u 1，infty}（x）$也是一个最佳策略。可以重复此扩展过程以获得最佳的k层再保险策略。最后，使用一些额外的适当准则估计最优多层再保险政策的未知参数。已经进行了三项基于模拟的研究，以证明：（{\\bf 1}）我们的研究结果的实际应用，以及（{\\bf 2}）如何使用其他适当的标准来估计最优多层合同的未知参数。多层再保险政策，类似于原来的止损再保险政策，在同样的意义上是最优的。此外，它还有一些原政策所没有的其他优化标准。在最小化一般平移单调风险测度$\\rho（\\cdot）$的{\\it或}保险人的总风险{\\it或}保险人和再保险人的总风险的最优准则下，本文（在讨论中）还将给定的最优再保险合同$\\f（\\cdot）$扩展到多层连续再保险保单。
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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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