Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks

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...

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Bibliographic Details
Published in:Methodology and computing in applied probability Vol. 24; no. 4; pp. 2557 - 2586
Main Authors: Germain, Maximilien, Mikael, Joseph, Warin, Xavier
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2022
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Business and Management
Differential equations
Economics
Electrical Engineering
Life Sciences
Machine learning
Mathematics
Mathematics and Statistics
Neural networks
Optimization and Control
Probability
Random variables
Statistics
MSC 68T07
Mean-field games
Neural networks
49N80
MSC 35Q89
Machine learning
MSC 65C30
Deep BSDE
McKean-Vlasov FBSDEs
machine learning
mean-field games
ISSN:1387-5841, 1573-7713
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-022-09946-1