A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations

By Jiongmin Yong. 2011

239 citations recorded by the source corpus.

A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field forward-backward stochastic differential equation. Using a decoupling technique, two Riccati differential equations are obtained, which are uniquely solvable under certain conditions. Then a feedback representation is obtained for the optimal control.

Subfields: Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/0efc64c7ab529343ea159a71150fb811230b07f9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. P. J. Graber
2. Jingrui Sun
3. Huyen Pham
4. Xunjing Li
5. Jianhui Huang

In Finance

1. Jingrui Sun
2. P. J. Graber
3. Dylan Possamaï
4. Xiaolu Tan
5. Jiongmin Yong
6. Huyen Pham
7. Xunjing Li
8. Mao Fabrice Djete

Citations in the corpus

• Stochastic Linear Quadratic Optimal Control Problems in Infinite Horizon (2016, methodology): “Recently, based on the work of Yong [24], Huang–Li–Yong [11] studied a mean-field LQ optimal control problem on [0,∞).”
• A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon (2012, methodology): “Then inspired by the results of [37], we obtain a system of algebraic Riccati equations (AREs, for short), whose solutions will lead us to the state feedback representation of the optimal control.”
• Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource (2016, methodology): “We use a technique developed by Yong in [60].”
• Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, background): “McKean-Vlasov context, the class of linear quadratic optimal control, which provides a typical case for solvable applications, has been studied in several papers, among them [24], [39], [25], [35], where the coefficients are assumed to be deterministic.”
• Bellman equation and viscosity solutions for mean-field stochastic control problem (2015, unknown): “This linear quadratic (LQ) framework is similar to the one in [38], and extends the one considered in [7] where there is no dependence on the law of the control, and the diffusion coefficient is deterministic.”
• McKean–Vlasov optimal control: The dynamic programming principle (2019, background): “Specialisations to linear–quadratic settings were also explored by Pham [65], Li, Sun, and Yong [57], Li, Sun, and Xiong [58], Huang, Li, and Yong [43], Yong [80], and Basei and Pham [8].”