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McKean–Vlasov BSDEs with Locally Monotone Coefficient

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Abstract

We consider a McKean Vlasov backward stochastic differential equation (MVBSDE) of the form

$${Y_t} = - F(t,{Y_t},{Z_t},[{Y_t}])\,dt + {Z_t}\,d{B_t},\,\,\,\,\,{Y_T} = \xi ,$$

where [Yt] stands for the law of Yt. We show that if F is locally monotone in y, locally Lipschitz with respect to z and law’s variable, and the monotonicity and Lipschitz constants κN, LN are such that \(L_N^2 + \kappa _N^ + = {\cal O}(\log (N))\), then the MVBSDE has a unique stable solution.

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Authors and Affiliations

  1. LIBMA, Faculty of Sciences Semlalia, Cadi Ayyad University, 2390, Marrakesh, Morocco

    Brahim Boufoussi

  2. École Supérieure de Technologie d’El Kelaa des Sraghna, Université Cadi Ayyad, Route de Béni Mellal Km 8, B. P. 104, El Kelaa des Sraghna, Morocco

    Soufiane Mouchtabih

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  1. Brahim Boufoussi
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  2. Soufiane Mouchtabih
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Correspondence to Soufiane Mouchtabih.

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Boufoussi, B., Mouchtabih, S. McKean–Vlasov BSDEs with Locally Monotone Coefficient. Acta. Math. Sin.-English Ser. 39, 1414–1424 (2023). https://doi.org/10.1007/s10114-023-1484-4

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  • DOI: https://doi.org/10.1007/s10114-023-1484-4

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