Generalized Finite Difference Methods for Risk-Averse Optimal Investment in Mean-Field Type Control

This work studies a finite-time mean-field type control problem arising from optimal investment under uncertainty with risk management. The problem leads to a nonlinearly coupled system of parabolic equations with temporal and nonlocal interactions. An explicit characterization of the solution to the system is obtained, and a generalized finite difference method (GFDM) combined with an iterative scheme is developed to ensure global temporal consistency of the mean-field feedback during backward computation. Numerical experiments illustrate the accuracy and effectiveness of the proposed approach.In addition, sensitivity studies with respect to the volatility and risk-aversion parameters demonstrate the robustness of the proposed numerical framework under parameter perturbations.