arXiv subjects

Nathan Sauldubois

Publications and source records attributed to Nathan Sauldubois.

4 recordsLinked to original sources

arXiv2026

Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs

We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context of optimal control and optimal stopping problems. Motivated by issues of sensitivity analysis in distributionally robust optimization (DRO) control and optimal stopping problems, we establish explicit formulas for the corresponding sensitivities under drift reference measure uncertainty. Our work is closely related to \citeauthor{bartl2023sensitivity} \cite{bartl2023sensitivity}. In contrast to the existing literature, our analysis is carried out within a general non-Markovian framework.

math.OC↗

arXiv2026

Projected McKean--Vlasov Dynamics for Entropic Weak Optimal Transport

Unlike classical optimal transport, weak transport costs depend nonlinearly on the conditional law of couplings. This feature is essential in problems involving barycenter, conditional moments, and martingale-type constraints. Meanwhile, such conditional dependence makes ordinary Wasserstein geometry insufficient and calls instead for an adapted Wasserstein viewpoint. In this paper, we investigate the entropy-regularized weak optimal transport via gradient flows in adapted Wasserstein space. We derive, from the formal tangent structure of adapted Wasserstein space and the projection onto the set of couplings with prescribed marginals, a coupled McKean--Vlasov SDE. A novel and subtle term is a projection that, at each $Y$-location, averages a weak-transport force that already depends on the conditional law of $Y$ given $X$, thereby preserving marginals while retaining the nonlinear weak-transport structure. Under mild integrability and regularity assumptions, we prove weak existence and uniqueness in law for this projected McKean--Vlasov equation. We then prove that the flow converges, in the adapted Wasserstein topology, to the unique minimizer of the entropic weak optimal transport problem. We also describe a particle approximation and illustrate the dynamics on optimal transport and martingale optimal transport examples.

math.PR↗

arXiv2026

Model Risk Static-Hedging a Constrained Distributionally Robust Optimization approach

We investigate model risk and distributionally robust optimization (DRO) under marginal and martingale constraints. Building on our previous work, we address the previously open case of static hedging with second-period maturity vanilla options and hedging strategies involving a vanilla payoff. We also extend recent sensitivity results to settings where admissible models must satisfy a martingale coupling constraint. Our approach relies on a weak implicit function theorem argument to construct families of measures satisfying the prescribed constraints. We derive closed-form sensitivity formulas and characterize the corresponding hedging strategies when the underlying process is real-valued.

math.PR↗

arXiv2025

First order Martingale model risk and semi-static hedging

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.

q-fin.MF↗