Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks

Methodology and Computing in Applied Probability - Tập 24 - Trang 2557-2586 - 2022
Maximilien Germain1,2,3, Joseph Mikael1, Xavier Warin1,4
1EDF R&D, Palaiseau, France
2Université de Paris, Paris, France
3LPSM, Paris, France
4FiME, Paris, France

Tóm tắt

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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Methodology and Computing in Applied Probability

Tập 24

2557-2586

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