Dynamic optimization problems for mean-field stochastic large-population systems

This paper considers dynamic optimization problems for a class of control average meanfield stochastic large-population systems. For each agent, the state system is governed by linear mean-field differential equation with individual noise and common noise, weight coefficients in corresponding cost functional can be indefinite. The decentralized optimal strategies are characterized Hamiltonian system, which turns out to an algebra forward-backward equation. Applying decoupling method, feedback representation further obtained through two Riccati equations. solvability equations under indefinite condition also derived. explicit structure limit related Nash certainty equivalence systems discussed some separation techniques. Moreover, proved satisfy approximate equilibrium property. good performance proposed theoretical results illustrated practical example from engineering field.