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Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks

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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.

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The datasets generated during the current study are available from the corresponding author on reasonable request

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Acknowledgements

This work is supported by FiME, Laboratoire de Finance des Marchés de l’Energie. We acknowledge the anonymous reviewers for their valuable suggestions which helped us to improve this work.

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Author notes

  1. Maximilien Germain, Joseph Mikael and Xavier Warin contributed equally to this work.

Authors and Affiliations

  1. EDF R&D, 7 Boulevard Gaspard Monge, Palaiseau, 91120, France

    Maximilien Germain, Joseph Mikael & Xavier Warin

  2. Université de Paris, Paris, France

    Maximilien Germain

  3. LPSM, Paris, France

    Maximilien Germain

  4. FiME, Paris, France

    Xavier Warin

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  1. Maximilien Germain
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  2. Joseph Mikael
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  3. Xavier Warin
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Correspondence to Maximilien Germain.

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Germain, M., Mikael, J. & Warin, X. Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks. Methodol Comput Appl Probab 24, 2557–2586 (2022). https://doi.org/10.1007/s11009-022-09946-1

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