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

By Jianhui Huang, Xunjing Li, Jiongmin Yong. 2012

131 citations recorded by the source corpus.

A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by the discussion of the well-posedness of the LQ problem. The optimal control can be expressed as a linear state feedback involving the state and its mean, through the solutions of two algebraic Riccati equations. The solvability of such kind of Riccati equations is investigated by means of semi-definite programming method.

Subfields: Computational Theory and Mathematics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/4639fd60baeb2532d1afb63cef35e4973b76a420

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

In Computational Theory and Mathematics

1. Jingrui Sun
2. Xiaolu Tan
3. Jiongmin Yong
4. Dylan Possamaï

In Finance

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

In Management Science and Operations Research

1. Jingrui Sun
2. Jiongmin Yong
3. Dylan Possamaï
4. Mao Fabrice Djete
5. Xiaolu Tan

Citations in the corpus

• Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, unknown): “In this 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 (Hu et al. 2012; Huang et al. 2015; Sun 2015; Yong 2013) where the coefficients are assumed to be deterministic.”
• Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, unknown): “Typical representatives include, but not limited to, McKean [27], Dawson [15], Chan [12], Buckdahn–Djehiche–Li–Peng [6], Buckdahn–Li–Peng [7], Borkar–Kumar [5], Crisan–Xiong [14], Andersson–Djehiche [2], Buckdahn–Djehiche–Li [8], MeyerBrandis–Oksendal–Zhou [28], Yong [35,36], Huang–Li–Yong [20], Li–”
• 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].”
• Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Open-Loop Solvabilities (2015, background): “Later, Huang–Li–Yong [16] generalized the results in [28] to the case with an infinite time horizon.”
• 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,∞).”
• Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability (2016, unknown): “See, for examples, McKean [16], Buckdahn–Djehiche–Li–Peng [5], Buckdahn–Li–Peng [6], Andersson–Djenhiche [2], Buckdahn–Djehiche–Li [4], Meyer-Brandis–Øksendal–Zhou [17], Yong [25], Elliott–Li–Ni [10], Cui–Li–Li [9], Huang–Li–Wang [11], Huang–Li–Yong [12].”