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.
From: Guojiang Shao [view email]
[v1]
Tue, 26 May 2026 09:02:13 UTC (454 KB)
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