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 inMethodology and computing in applied probability Vol. 24; no. 4; pp. 2557 - 2586
Main Authors Germain, Maximilien, Mikael, Joseph, Warin, Xavier
Format Journal Article
LanguageEnglish
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
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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
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-022-09946-1