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Forward and backward stochastic differential equations with normal constraints in law

Author

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  • Briand, Philippe
  • Cardaliaguet, Pierre
  • Chaudru de Raynal, Paul-Éric
  • Hu, Ying

Abstract

In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding “normal” vector. We also study the associated interacting particle system reflected in mean field and asymptotically described by such equations. The case of particles submitted to a common noise as well as the asymptotic system is studied in the forward case. Eventually, we connect the forward and backward stochastic differential equations with normal constraints in law with partial differential equations stated on the Wasserstein space and involving a Neumann condition in the forward case and an obstacle in the backward one.

Suggested Citation

  • Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:12:p:7021-7097
    DOI: 10.1016/j.spa.2020.07.007
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    References listed on IDEAS

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    1. Philippe Briand & Romuald Elie & Ying Hu, 2018. "BSDEs with mean reflection," Post-Print hal-01318649, HAL.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    3. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
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    Cited by:

    1. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    2. Cui, Fengfeng & Zhao, Weidong, 2023. "Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 193(C).

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