英文标题：
《Optimal insurance purchase strategies via optimal multiple stopping
  times》
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作者：
Rodrigo S. Targino, Gareth W. Peters, Georgy Sofronov, Pavel V.
  Shevchenko
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最新提交年份：
2013
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英文摘要：
  In this paper we study a class of insurance products where the policy holder has the option to insure $k$ of its annual Operational Risk losses in a horizon of $T$ years. This involves a choice of $k$ out of $T$ years in which to apply the insurance policy coverage by making claims against losses in the given year. The insurance product structure presented can accommodate any kind of annual mitigation, but we present three basic generic insurance policy structures that can be combined to create more complex types of coverage. Following the Loss Distributional Approach (LDA) with Poisson distributed annual loss frequencies and Inverse-Gaussian loss severities we are able to characterize in closed form analytical expressions for the multiple optimal decision strategy that minimizes the expected Operational Risk loss over the next $T$ years. For the cases where the combination of insurance policies and LDA model does not lead to closed form expressions for the multiple optimal decision rules, we also develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.
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中文摘要：
在本文中，我们研究了一类保险产品，其中投保人有权在$T$年的期限内为$k$的年度操作风险损失投保。这涉及到从$T$年中选择$k$年，通过对给定年份的损失提出索赔来应用保单覆盖范围。本文介绍的保险产品结构可以适应任何类型的年度缓解措施，但我们介绍了三种基本的通用保险单结构，它们可以组合起来创建更复杂的保险类型。按照泊松分布的年度损失频率和逆高斯损失严重度的损失分布法（LDA），我们能够在封闭形式的分析表达式中描述多个最优决策策略的特征，以最小化未来$T$年的预期操作风险损失。对于保险单和LDA模型的组合不会导致多个最优决策规则的闭式表达式的情况，我们还开发了一类原则性的最优决策规则的闭式近似。这些近似是基于年损失复合过程分布和年损失函数的一类正交Askey多项式级数基展开表示而发展起来的。
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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：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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