Paper: arXiv 2410.06906

Authors: Nathan Sauldubois, Nizar Touzi

Abstract

We investigate model risk distributionally robust sensitivities for functionals on the Wasserstein space when the underlying model is constrained to the martingale class and/or is subject to constraints on the first marginal law. Our results extend the findings of Bartl, Drapeau, Obloj & Wiesel \cite{bartl2021sensitivity} and Bartl & Wiesel \cite{bartlsensitivityadapted} by introducing the minimization of the distributionally robust problem with respect to semi-static hedging strategies. We provide explicit characterizations of the model risk (first order) optimal semi-static hedging strategies. The distributional robustness is analyzed both in terms of the adapted Wasserstein metric and the more relevant standard Wasserstein metric.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents highly sophisticated theoretical work extending distributionally robust optimization (DRO) to semi-static hedging using Wasserstein metrics and optimal transport theory. However, it is primarily a theoretical paper with heavy functional analysis and minimal empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Model risk sensitivity & optimal semi-static hedging under martingale constraints] --> B[Inputs: Functionals on Wasserstein space & First marginal law constraints]
    B --> C[Framework Setup: Adapted & Standard Wasserstein metrics]
    C --> D[Optimization: Minimize distributionally robust problem with semi-static hedging]
    D --> E[Outcome: Extension of Bartl et al. results to semi-static strategies]
    D --> F[Outcome: Explicit characterization of first-order optimal hedging strategies]

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