| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 41 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2019057 | |
| Published online | 30 June 2020 | |
On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems*
School of Mathematics, Sichuan University,
Chengdu
610065, P.R. China.
** Corresponding author: xiaotian2008001@gmail.com
Received:
15
February
2019
Accepted:
18
September
2019
This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.
Mathematics Subject Classification: 93E20 / 49N10 / 49N70
Key words: Mean-field linear-quadratic optimal control problems / time inconsistency / closed-loop equilibrium strategies / Riccati system
© EDP Sciences, SMAI 2020
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