Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Open-Loop Solvabilities
By Jingrui Sun. 2015
66 citations recorded by the source corpus.
This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ problem, whereas uniform convexity of the cost functional is sufficient for the open-loop solvability of the problem. By considering a family of uniformly convex cost functionals, a characterization of the finiteness of the problem is derived and a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Then, it is proved that the uniform convexity of the cost functional is equivalent to the solvability of two coupled differential Riccati equations and the unique open-loop optimal control admits a state feedback representation in the case that the cost functional is uniformly convex. Finally, some examples are presented to illustrate the theory developed.
Subfields: Demography, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/567350fdeeaed8f1ba63d3b2b5cdfd55e8e56f6c
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Citations in the corpus
- Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, unknown): “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.”
- Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, unknown): “Bensoussan, A., Sung, K.C.J., Yam, S.C.P., Yung, S.P.: Linear-quadratic mean field games.”
- Stochastic Linear Quadratic Optimal Control Problems in Infinite Horizon (2016, background): “Keywords Stochastic linear quadratic optimal control · Stabilizability · Open-loop solvability · Closed-loop solvability · Algebraic Riccati equation · Static stabilizing solution · Closed-loop representation AMS Subject Classifications 49N10 · 49N35 · 93D15 · 93E20 B Jingrui Sun sjr@mail.ustc.edu.c”