英文标题：
《Computational aspects of robust optimized certainty equivalents and
option pricing》
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作者：
Daniel Bartl, Samuel Drapeau, Ludovic Tangpi
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最新提交年份：
2019
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英文摘要：
Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome for the so-called optimized certainty equivalent risk measure (OCE) -- including the average value-at-risk as a special case. First we focus on the case where the uncertainty is modeled by a nonlinear expectation penalizing distributions that are \"far\" in terms of optimal-transport distance (Wasserstein distance for instance) from a given baseline distribution. It turns out that the computation of the robust OCE reduces to a finite dimensional problem, which in some cases can even be solved explicitly. This principle also applies to the shortfall risk measure as well as for the pricing of European options. Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions. Finally, we give conditions on the latter set under which the robust average value-at-risk is a tail risk measure.
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中文摘要：
考虑到风险管理和期权定价中的模型不确定性，会导致无限维优化问题，这些问题在分析和数值上都很难解决。在本文中，我们研究了所谓的优化确定性等效风险度量（OCE）何时可以克服这一障碍，包括作为特例的平均风险值。首先，我们将重点放在不确定性由非线性期望惩罚分布建模的情况，该分布与给定基线分布的最佳运输距离（例如Wasserstein距离）相比“远”。结果表明，鲁棒OCE的计算简化为有限维问题，在某些情况下甚至可以显式求解。这一原则也适用于短缺风险度量以及欧洲期权的定价。此外，我们推导了可测索赔的鲁棒OCE的凸对偶表示，无需对分布集进行任何假设。最后，我们给出了后一个集的条件，在此条件下，鲁棒平均风险值是尾部风险度量。
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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：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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