Backward Mean-Field Linear-Quadratic-Gaussian (LQG) Games: Full and Partial Information

2016 ◽  
Vol 61 (12) ◽  
pp. 3784-3796 ◽  
Author(s):  
Jianhui Huang ◽  
Shujun Wang ◽  
Zhen Wu
Keyword(s):  
Partial Information ◽  
Mean Field ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian

scholarly journals Mean field approach to stochastic control with partial information

2021 ◽  
Author(s):  
Alain Bensoussan ◽  
Phillip Yam
Keyword(s):  
Partial Information ◽  
Mean Field Theory ◽  
Mean Field ◽  
Initial Distribution ◽  
Linear Quadratic ◽  
Gaussian Case ◽  
Hamilton Jacobi Bellman ◽  
Non Gaussian ◽  
Initial Distributions ◽  
Quadratic Case

In our present article, we follow our way of developing mean field type control theory in our earlier works [4], by first introducing the Bellman and then master equations, the system of Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) equations, and then tackling them by looking for the semi-explicit solution for the linear quadratic case, especially with an arbitrary initial distribution; such a problem, being left open for long, has not been specifically dealt with in the earlier literature, such as [3, 13], which only tackled the linear quadratic setting with Gaussian initial distributions. Thanks to the effective mean-field theory, we propose a solution to this long standing problem of the general non-Gaussian case. Besides, our problem considered here can be reduced to the model in [2], which is fundamentally different from our present proposed framework.

scholarly journals Linear-Quadratic-Gaussian mean-field controls of social optima

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhenghong Qiu ◽  
Jianhui Huang ◽  
Tinghan Xie
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Backward Stochastic Differential Equation ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Individual Agent ◽  
State Process ◽  
Weakly Coupled

<p style='text-indent:20px;'>This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be <i>indefinite</i> in cost functional. This setup is innovative and has great theoretical and realistic significance as its applications in mathematical finance (e.g., portfolio selection in mean-variation model). Using some <i>fully-coupled</i> variational analysis under the person-by-person optimality principle, and the mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with <i>embedding representation</i>. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.</p>

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