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Sensitivity of functionals of McKean-Vlasov SDEs with respect to the initial distribution

Author

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  • de Feo, Filippo
  • Federico, Salvatore
  • Gozzi, Fausto
  • Touzi, Nizar

Abstract

We examine the sensitivity at the origin of the distributional robust optimization problem in the context of a model generated by a mean field stochastic differential equation. We adapt the finite dimensional argument developed by Bartl, Drapeau, Obloj, & Wiesel to our framework involving the infinite dimensional gradient of the solution of the mean field SDE with respect to its initial data. We revisit the derivation of this gradient process as previously introduced by Buckdahn, Li, Peng, & Rainer and we complement the existing properties so as to satisfy the requirement of our main result. We use the theory developed in the context of a mean-field systemic risk model by evaluating the sensitivity with respect to the initial distribution for the variance of the log-monetary reserve of a representative bank.

Suggested Citation

  • de Feo, Filippo & Federico, Salvatore & Gozzi, Fausto & Touzi, Nizar, 2026. "Sensitivity of functionals of McKean-Vlasov SDEs with respect to the initial distribution," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:spapps:v:195:y:2026:i:c:s0304414925003126
    DOI: 10.1016/j.spa.2025.104868
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    References listed on IDEAS

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    1. Daniel Bartl & Samuel Drapeau & Jan Obloj & Johannes Wiesel, 2020. "Sensitivity analysis of Wasserstein distributionally robust optimization problems," Papers 2006.12022, arXiv.org, revised Nov 2021.
    2. Daniel Zhuoyu Long & Jin Qi & Aiqi Zhang, 2024. "Supermodularity in Two-Stage Distributionally Robust Optimization," Management Science, INFORMS, vol. 70(3), pages 1394-1409, March.
    3. Jose Blanchet & Lin Chen & Xun Yu Zhou, 2022. "Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances," Management Science, INFORMS, vol. 68(9), pages 6382-6410, September.
    4. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    5. Yueyao Li & Wenxun Xing, 2024. "Globalized distributionally robust optimization based on samples," Journal of Global Optimization, Springer, vol. 88(4), pages 871-900, April.
    6. Jose Blanchet & Karthyek Murthy, 2019. "Quantifying Distributional Model Risk via Optimal Transport," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 565-600, May.
    Full references (including those not matched with items on IDEAS)

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