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Solvability of Infinite Horizon McKean–Vlasov FBSDEs in Mean Field Control Problems and Games

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Abstract

In this paper, we show existence and uniqueness of solutions of the infinite horizon McKean–Vlasov FBSDEs using two different methods, which lead to two different sets of assumptions. We use these results to solve the infinite horizon mean field type control problems and mean field games.

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Funding

Funding was provided by Directorate for Mathematical and Physical Sciences (Grant No. DMS-2106556).

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, USA

    Erhan Bayraktar

  2. Department of Mathematics, University of Vienna, Vienna, Austria

    Xin Zhang

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  1. Erhan Bayraktar
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  2. Xin Zhang
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Correspondence to Erhan Bayraktar.

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E. Bayraktar is partially supported by the National Science Foundation under grant DMS-2106556 and by the Susan M. Smith chair.

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Bayraktar, E., Zhang, X. Solvability of Infinite Horizon McKean–Vlasov FBSDEs in Mean Field Control Problems and Games. Appl Math Optim 87, 13 (2023). https://doi.org/10.1007/s00245-022-09926-4

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  • DOI: https://doi.org/10.1007/s00245-022-09926-4

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