Linear-quadratic McKean-Vlasov stochastic control problems with random coefficients on finite and infinite horizon, and applications

Understand

We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems.

• We study both finite-horizon and infinite-horizon problems, and allow notably some coefficients to be stochastic.
• Our method is based on a suitable extension of the martingale formulation for verification theorems in control theory.
• The optimal control involves the solution to a system of Riccati ordinary differential equations and to a linear mean-field backward stochastic differential equation, existence and uniqueness conditions are provided for such a system.