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Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks

Author

Listed:
  • Maximilien Germain

    (EDF R&D
    Université de Paris
    LPSM)

  • Joseph Mikael

    (EDF R&D)

  • Xavier Warin

    (EDF R&D
    FiME)

Abstract

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations (FBSDEs). Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems. As a consequence, we obtain methods able to tackle both mean-field games and mean-field control problems in moderate dimension. We analyze the numerical behavior of our algorithms on several multidimensional examples including non linear quadratic models.

Suggested Citation

  • Maximilien Germain & Joseph Mikael & Xavier Warin, 2022. "Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2557-2586, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09946-1
    DOI: 10.1007/s11009-022-09946-1
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    References listed on IDEAS

    as
    1. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    2. Huyên Pham & Xavier Warin & Maximilien Germain, 2021. "Neural networks-based backward scheme for fully nonlinear PDEs," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-24, February.
    3. Ren'e Carmona & Mathieu Lauri`ere, 2021. "Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance," Papers 2107.04568, arXiv.org.
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