Risk measures based on weak optimal transport

Kupper, Michael; Nendel, Max und Sgarabottolo, Alessandro (2. Oktober 2024): Risk measures based on weak optimal transport. In: Quantitative Finance, Bd. 25, Nr. 2: S. 163-180

Abstract

In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we discuss computational aspects related to the nonlinear transform as well as approximations of the risk measures using, for example, neural networks. Our setup comprises a variety of examples, such as classical optimal transport penalties, parametric families of models, divergence risk measures, uncertainty on path spaces, moment constraints, and martingale constraints. In a last step, we show how to use the theoretical results for the numerical computation of worst-case losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1469-7688
• Bemerkung: Special Issue on XXIV Workshop on Quantitative Finance
• Sprache: Englisch