TY - JOUR

T1 - Computational aspects of robust optimized certainty equivalents and option pricing

AU - Bartl, Daniel

AU - Drapeau, Samuel

AU - Tangpi, Ludovic

N1 - Publisher Copyright:
© 2019 Wiley Periodicals, Inc.

PY - 2020/1

Y1 - 2020/1

N2 - 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.

AB - 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.

KW - q-fin.RM

KW - math.OC

KW - 91G80, 90B50, 60E10, 91B30

KW - robust option pricing

KW - average value-at-risk

KW - distribution uncertainty

KW - optimal transport

KW - penalization

KW - Wasserstein distance

KW - convex duality

KW - optimized certainty equivalent

UR - http://www.scopus.com/inward/record.url?scp=85062950968&partnerID=8YFLogxK

U2 - 10.1111/mafi.12203

DO - 10.1111/mafi.12203

M3 - Article

VL - 30

SP - 287

EP - 309

JO - Mathematical Finance: an international journal of mathematics, statistics and financial economics

JF - Mathematical Finance: an international journal of mathematics, statistics and financial economics

SN - 0960-1627

IS - 1

ER -