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http://hdl.handle.net/10397/70386
Title: | Mean-field stochastic linear quadratic optimal control problems : closed-loop solvability | Authors: | Li, X Sun, JR Yong, JM |
Issue Date: | 2016 | Source: | Probability uncertainty and quantitative risk, 2016, v. 1, 2, p. 1-24 | Abstract: | 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. | Keywords: | Mean-field stochastic differential equation Linear quadratic optimal control Riccati equation Regular solution Closed-loop solvability |
Publisher: | Springer | Journal: | Probability uncertainty and quantitative risk | ISSN: | 2367-0126 | DOI: | 10.1186/s41546-016-0002-3 | Rights: | © The Author(s). 2016 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The following publication Li, X., Sun, J. R., & Yong, J. M. (2016). Mean-field stochastic linear quadratic optimal control problems : closed-loop solvability. Probability Uncertainty and Quantitative Risk, 1, 2, 1-24 is available at https://dx.doi.org/10.1186/s41546-016-0002-3 |
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