Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional

Lin Li; Jiongmin Yong

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arXiv · 2601.21748

Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional

Lin Li·Jiongmin Yong

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Abstract

This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It involves BSDEs in $L^1$ whose well-posedness is a subtle issue. A suitable framework has been adopted so that the corresponding LQ problem is correctly formulated. Open-loop and closed-loop solvability of such an LQ problem have been investigated and characterized by the solvability of an FBSDE and that of Riccati differential equation.

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BibTeX RIS

Lin Li, Jiongmin Yong. 2026-01-29. Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional. https://arxiv.org/abs/2601.21748

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