Year: 2018
Type: preprint
Abstract: Recently it has been found that for a stochastic linear-quadratic optimal control problem (LQ problem, for short) in a finite horizon, open-loop solvability is strictly weaker than closed-loop solvability which is equivalent to the regular solvability of the corresponding Riccati equation. Therefore, when an LQ problem is merely open-loop solvable not closed-loop solvable, which is possible, the usual Riccati equation approach will fail to produce a state feedback representation of open-loop optimal controls. The objective of this paper is to introduce and investigate the notion of weak closed-loop optimal strategy for LQ problems so that its existence is equivalent to the open-loop solvability of the LQ problem. Moreover, there is at least one open-loop optimal control admitting a state feedback representation. Finally, we present an example to illustrate the procedure for finding weak closed-loop optimal strategies.
Source: arXiv (Cornell University)
Authors: Sun, Jingrui, Wang, Hanxiao, Yong, Jiongmin
Institutions: University of Central Florida, Fudan University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2808713175