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Mean-field games with unbounded controls: a weak formulation approach to global solutions

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  • Ulrich Horst
  • Takashi Sato

Abstract

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach does not require boundedness assumptions on the model parameters or time horizons and allows for running costs that are quadratic in the control variable.

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  • Ulrich Horst & Takashi Sato, 2026. "Mean-field games with unbounded controls: a weak formulation approach to global solutions," Papers 2603.05624, arXiv.org.
    • Handle: RePEc:arx:papers:2603.05624
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    References listed on IDEAS

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    7. Imkeller, Peter & Dos Reis, Gonçalo, 2010. "Path regularity and explicit convergence rate for BSDE with truncated quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 348-379, March.
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    9. Guanxing Fu & Paulwin Graewe & Ulrich Horst & Alexandre Popier, 2021. "A Mean Field Game of Optimal Portfolio Liquidation," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1250-1281, November.
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