Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability

By Xunjing Li, Jingrui Sun, Jiongmin Yong. 2016

65 citations recorded by the source corpus.

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic. Closed-loop strategies are introduced, which require to be independent of initial states; and such a nature makes it very useful and convenient in applications. In this paper, the existence of an optimal closed-loop strategy for the system (also called the closed-loop solvability of the problem) is characterized by the existence of a regular solution to the coupled two (generalized) Riccati equations, together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/dd86b622a43490d627a2fa1fffe3622395088bab

How researchers see this paper

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

In Demography

1. Jiongmin Yong
2. Jingrui Sun
3. Mao Fabrice Djete
4. Xiaolu Tan
5. 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 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–”
• Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, unknown): “This class of semi closed-loop control extends the class of closed-loop strategies for the LQ control of McKeanVlasov equations (or mean-field stochastic differential equations) without common noise W 0, as recently studied in (Li et al. 2016) where the controls are chosen at any time t in linear fo”
• 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].”
• Stochastic Linear Quadratic Optimal Control Problems in Infinite Horizon (2016, background): “See Yong [24], Sun [17], and Li–Sun–Yong [13] for relevant works of LQ problems involving mean-field.”