Investment optimization in the Heston model

The investment portfolio optimization problem in the Heston model is solved via several reductions. Namely, we reduce the original problem to the Cauchy problem for a new fully nonlinear parabolic equation and construct its probabilistic representation via solution of a forward–backward stochastic differential equation (FBSDE). Next we reduce solution of the FBSDE to a new optimization problem and construct its numerical solution applying the neural network technique.