Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks

Maximilien Germain (), Joseph Mikael () and Xavier Warin ()
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Maximilien Germain: EDF R&D
Joseph Mikael: EDF R&D
Xavier Warin: EDF R&D

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2557-2586

Abstract: 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.

Keywords: Neural networks; McKean-Vlasov FBSDEs; Deep BSDE; Mean-field games; Machine learning; MSC 65C30; MSC 68T07; 49N80; MSC 35Q89 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-022-09946-1

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