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http://hdl.handle.net/10397/93912
Title: | Linear quadratic optimal control problems for mean-field backward stochastic differential equations | Authors: | Li, X Sun, J Xiong, J |
Issue Date: | Aug-2019 | Source: | Applied mathematics and optimization, Aug. 2019, v. 80, no. 1, p. 223-250 | Abstract: | This paper is concerned with linear quadratic optimal control problems for mean-field backward stochastic differential equations (MF-BSDEs, for short) with deterministic coefficients. The optimality system, which is a linear mean-field forward–backward stochastic differential equation with constraint, is obtained by a variational method. By decoupling the optimality system, two coupled Riccati equations and an MF-BSDE are derived. It turns out that the coupled two Riccati equations are uniquely solvable. Then a complete and explicit representation is obtained for the optimal control. | Keywords: | Decoupling Linear quadratic optimal control Mean-field backward stochastic differential equation Optimality system Riccati equation |
Publisher: | Springer | Journal: | Applied mathematics and optimization | ISSN: | 0095-4616 | EISSN: | 1432-0606 | DOI: | 10.1007/s00245-017-9464-7 | Rights: | © Springer Science+Business Media, LLC 2017 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00245-017-9464-7 |
Appears in Collections: | Journal/Magazine Article |
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Li_Linear_Quadratic_Optimal.pdf | Pre-Published version | 908.79 kB | Adobe PDF | View/Open |
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