Work

Decentralized Strategies for Backward Linear‐Quadratic Mean Field Games and Teams

Year: 2025

Type: article

Abstract: ABSTRACT This paper studies a new class of linear‐quadratic mean field games and teams problem, where the large‐population system satisfies a class of weakly coupled linear backward stochastic differential equations (BSDEs), and (a part of solution of BSDE) enter the state equations and cost functionals. Inspired by the stochastic control problem with partial information, we adopt the backward separation approach to solve the problem. By virtue of the stochastic maximum principle and optimal filter technique, we obtain a Hamiltonian system first, which is a fully coupled forward‐backward stochastic differential equation (FBSDE). And then, by decoupling the Hamiltonian system, we derive a feedback form optimal strategy by introducing Riccati equations, stochastic differential equation (SDE), and BSDE. Finally, we provide a numerical example to simulate our results.

Source: Optimal Control Applications and Methods

DOI: 10.1002/oca.3320

Authors: Yu Si, Jingtao Shi

Institution: Shandong University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: Natural Science Foundation of Shandong Province, National Key Research and Development Program of China

Awards: G17409056, G5202198833, G6939085221