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arXiv · 2605.26721

Stochastic LQ Optimal Control with Random Coefficients and a Terminal Mean-Field Cost

Guojiang Shao·Zuo Quan Xu·Qi Zhang
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Abstract

This paper investigates a multidimensional non-homogeneous stochastic linear-quadratic optimal control problem featuring random coefficients and a terminal mean-field term in the cost functional, enabling its direct application to mean-variance models in financial engineering. Employing the Lagrangian duality method together with a decomposition approach for linear backward stochastic differential equations, we provide two types of sufficient conditions for solvability and derive the corresponding optimal controls. In particular, in the deterministic-coefficient case, our condition is weaker than the standard condition found in the existing literature on mean-field stochastic LQ problems. Finally, a numerical example drawn from optimal portfolio selection with multiple assets under mean-variance utility demonstrates the applicability of our results.

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Guojiang Shao, Zuo Quan Xu, Qi Zhang. 2026-05-26. Stochastic LQ Optimal Control with Random Coefficients and a Terminal Mean-Field Cost. https://arxiv.org/abs/2605.26721

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