Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks - Germain, Maximilien; Mikael, Joseph; Warin, Xavier (Methodology and computing in applied probability, 2022)
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.