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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Vydáno v:Methodology and computing in applied probability Ročník 24; číslo 4; s. 2557 - 2586
Hlavní autoři: Germain, Maximilien, Mikael, Joseph, Warin, Xavier
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2022
Springer Nature B.V
Springer Verlag
Témata:
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
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Popis
Shrnutí: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.
Bibliografie: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