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Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts

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  • Adams, Daniel
  • dos Reis, Gonçalo
  • Ravaille, Romain
  • Salkeld, William
  • Tugaut, Julian

Abstract

We study reflected McKean–Vlasov diffusions over a convex, non-bounded domain with self-stabilising coefficients that do not satisfy the classical Wasserstein Lipschitz condition. We establish existence and uniqueness results for this class and address the propagation of chaos. Our results are of wider interest: without the McKean–Vlasov component they extend reflected SDE theory, and without the reflective term they extend the McKean–Vlasov theory.

Suggested Citation

  • Adams, Daniel & dos Reis, Gonçalo & Ravaille, Romain & Salkeld, William & Tugaut, Julian, 2022. "Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 264-310.
    • Handle: RePEc:eee:spapps:v:146:y:2022:i:c:p:264-310
    DOI: 10.1016/j.spa.2021.12.017
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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. Ramasubramanian, S., 2006. "An insurance network: Nash equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 374-390, April.
    3. Benachour, S. & Roynette, B. & Talay, D. & Vallois, P., 1998. "Nonlinear self-stabilizing processes - I Existence, invariant probability, propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 173-201, July.
    4. Zheng Han & Yaozhong Hu & Chihoon Lee, 2016. "Optimal pricing barriers in a regulated market using reflected diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 639-647, April.
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    Cited by:

    1. Fan, Xiliang & Yu, Ting & Yuan, Chenggui, 2023. "Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 383-415.
    2. Chen, Xingyuan & dos Reis, Gonçalo, 2022. "A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Ning, Ning & Wu, Jing & Zheng, Jinwei, 2024. "One-dimensional McKean–Vlasov stochastic variational inequalities and coupled BSDEs with locally Hölder noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 171(C).

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