A Unified Theory of Solvability for Stochastic Linear-Quadratic Control Problems I: The Homogeneous Case

Hongwei Mei · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27579 · open-access PDF

Abstract

The existing theory of stochastic linear-quadratic (LQ) optimal control problems focuses on open-loop and closed-loop solvability. For finite horizon problems, it is widely accepted that those two types of solvability are not equivalent in general, as demonstrated by explicit counterexamples. In contrast, they coincide in standard infinite-horizon formulations with constant coefficients under suitable stabilizability and integrability assumptions. This paper aims at challenging this well-established paradigm by developing a novel framework of closed-loop solvability, namely generalized closed-

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