Accounting for model uncertainty in risk management  leads to infinite dimensional optimization problems which are both analytically and numerically untractable . In this article we study when this fact 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 set of possible distributions of a financial loss is given by the neighborhood of a given baseline distribution in the Wasserstein distance, or more generally, an optimal-transport distance. Here 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.  Further, we derive convex dual representations of the robust OCE for measurable claims without any assumptions on the set of distributions and finally give conditions on the latter set under which the robust average value-at-risk is a tail risk measure.
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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and option pricing
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untractable
intractable
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fact
hurdle
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-
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set of possible distributions of a financial loss is given by the neighborhood of
uncertainty is modeled by a nonlinear expectation penalizing distributions that are "far" in terms of optimal-transport distance (Wasserstein distance for instance) from
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in the Wasserstein distance, or more generally, an optimal-transport distance. Here it
. It
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This principle also applies to the shortfall risk measure as well as for the pricing of European options.
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and finally
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