IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v188y2025ics0304414925001103.html

A propagation of chaos result for weakly interacting nonlinear Snell envelopes

Author

Listed:
  • Djehiche, Boualem
  • Dumitrescu, Roxana
  • Zeng, Jia

Abstract

In this article, we establish a propagation of chaos result for weakly interacting nonlinear Snell envelopes which converge to a class of mean-field reflected backward stochastic differential equations (BSDEs) with jumps and right-continuous and left-limited obstacle, where the mean-field interaction in terms of the distribution of the Y-component of the solution enters both the driver and the lower obstacle. Under mild Lipschitz and integrability conditions on the coefficients, we prove existence and uniqueness of the solution to both the mean-field reflected BSDEs with jumps and the corresponding system of weakly interacting particles by using a new approach relying on the characterization of the solution of a mean-field reflected BSDE in terms of a nonlinear optimal stopping problem of mean-field type. We then provide a propagation of chaos result for the whole solution (Y,Z,U,K), which requires new technical results due to the dependence of the obstacle on the solution and the presence of jumps. In particular, we obtain a new law of large number type result for right-continuous and left-limited processes.

Suggested Citation

  • Djehiche, Boualem & Dumitrescu, Roxana & Zeng, Jia, 2025. "A propagation of chaos result for weakly interacting nonlinear Snell envelopes," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001103
    DOI: 10.1016/j.spa.2025.104669
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925001103
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104669?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Briand, Philippe & Hibon, Hélène, 2021. "Particles Systems for mean reflected BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 253-275.
    2. Shkolnikov, Mykhaylo, 2012. "Large systems of diffusions interacting through their ranks," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1730-1747.
    3. 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.
    4. 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.
    5. Chenguang Liu & Antonis Papapantoleon & Alexandros Saplaouras, 2024. "Convergence rates for Backward SDEs driven by L\'evy processes," Papers 2402.01337, arXiv.org.
    6. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    7. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    8. Roxana Dumitrescu & Marie-Claire Quenez & Agnès Sulem, 2015. "Optimal Stopping for Dynamic Risk Measures with Jumps and Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 219-242, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Hanwu, 2024. "Backward stochastic differential equations with double mean reflections," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    2. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
    3. Qian, Hongchao, 2025. "Mean reflected backward stochastic differential equations with jumps in a convex domain," Statistics & Probability Letters, Elsevier, vol. 223(C).
    4. Dai, Yin & Li, Ruinan, 2021. "Transportation cost inequality for backward stochastic differential equations with mean reflection," Statistics & Probability Letters, Elsevier, vol. 177(C).
    5. Cui, Fengfeng & Zhao, Weidong, 2023. "Well-posedness of mean reflected BSDEs with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 193(C).
    6. Bensoussan, A. & Yam, S.C.P. & Zhang, Z., 2015. "Well-posedness of mean-field type forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3327-3354.
    7. Ying Hu & Remi Moreau & Falei Wang, 2024. "General Mean Reflected Backward Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(1), pages 877-904, March.
    8. Niu, Yue & Qu, Baoyou & Wang, Falei, 2025. "Lp-solutions of multi-dimensional BSDEs with mean reflection," Stochastic Processes and their Applications, Elsevier, vol. 187(C).
    9. Lin, Yiqing & Xu, Kun, 2025. "Propagation of chaos for mean-field reflected BSDEs with jumps," Statistics & Probability Letters, Elsevier, vol. 221(C).
    10. Yu, Xianye & Zhang, Mingbo, 2020. "Backward stochastic differential equations driven by fractional noise with non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 159(C).
    11. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    12. Damiano Brigo & Marco Francischello & Andrea Pallavicini, 2015. "Invariance, existence and uniqueness of solutions of nonlinear valuation PDEs and FBSDEs inclusive of credit risk, collateral and funding costs," Papers 1506.00686, arXiv.org, revised Nov 2015.
    13. Menozzi, Stéphane, 2018. "Martingale problems for some degenerate Kolmogorov equations," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 756-802.
    14. David Itkin & Martin Larsson, 2021. "On A Class Of Rank-Based Continuous Semimartingales," Papers 2104.04396, arXiv.org.
    15. Umut c{C}etin & Albina Danilova, 2014. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems," Papers 1407.2420, arXiv.org, revised Sep 2016.
    16. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Annals of Finance, Springer, vol. 11(2), pages 151-198, May.
    17. Wu, Zhen & Xu, Ruimin, 2019. "Probabilistic interpretation for Sobolev solutions of McKean–Vlasov partial differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 273-283.
    18. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    19. Fu, Zongkui & Fei, Dandan, 2025. "General mean-field reflected backward stochastic differential equations with locally monotone coefficients," Statistics & Probability Letters, Elsevier, vol. 216(C).
    20. Dianetti, Jodi, 2023. "Strong Solutions to Submodular Mean Field Games with Common Noise and Related McKean-Vlasov FBSDES," Center for Mathematical Economics Working Papers 674, Center for Mathematical Economics, Bielefeld University.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001103. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.