Backward Linear-Quadratic Mean Field Social Optima with Partial Information

Abstract

This paper is concerned with the linear-quadratic social optima for a class of N weakly coupled backward system with partial information structure. The system dynamics are governed by linear backward stochastic differential equations, and the objective is to minimize a social cost. The stochastic filtering Hamiltonian system is obtained from variational analysis. By virtue of the stochastic filtering technique and backward decoupling method, the feedback form of optimal control is derived. Aiming to overcome the curse of dimensionality and reduce the information requirements, we design a set of decentralized control laws, which is further shown to be asymptotic. Finally, an example of the scalar-valued case is studied.

Keywords

Mean field game / Social optima / Forward–backward stochastic differential equation / Riccati equation / Partial information / Direct method / 60H10 / 91A15 / 93E11

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Funding

National Natural Science Foundation of China(11831010)

Natural Science Foundation of Shandong Province(ZR2019ZD42)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature