Numerical resolution of McKean-Vlasov FBSDEs using neural networks

Abstract

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. 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 examples including non linear quadratic models.

arXiv comment29 pages, revised version, to appear in Methodology and Computing in Applied Probability