Accounting for model uncertainty in risk management and option pricing leads to infinite‐dimensional optimization problems that are both analytically and numerically intractable. In this article, we study when this hurdle can be overcome for the so‐called optimized certainty equivalent (OCE) risk measure—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 that penalizes distributions that are “far” in terms of optimal‐transport distance (e.g. Wasserstein distance) 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.

中文翻译：

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健壮的确定性当量和期权定价的计算方面

在风险管理和期权定价中考虑模型不确定性会导致在分析和数值上都难以解决的无限维优化问题。在本文中，我们研究了何时可以通过所谓的最佳确定性当量（OCE）风险衡量标准克服此障碍，包括作为特殊情况的平均风险价值。首先，我们关注的情况是，不确定性是通过非线性期望来建模的，该期望期望根据给定基线分布的最佳运输距离（例如Wasserstein距离）对“远”的分布进行惩罚。事实证明，健壮的OCE的计算可简化为有限维问题，在某些情况下甚至可以明确解决。该原则也适用于短缺风险度量以及欧洲期权的定价。进一步，我们得出可衡量索赔的稳健OCE的凸对偶表示，而无需对分布集进行任何假设。最后，我们在后一组条件下给出稳健的平均风险值是尾部风险度量的条件。