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arXiv · 2406.04621

Mean-field stochastic linear quadratic control problem with random coefficients

Jie Xiong·Wen Xu
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Abstract

In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this optimal control by an optimality system. However, because of the term of the form $\mathbb{E}[A_1(\cdot)^\top Y(\cdot)] $ in the adjoint equation, which cannot be represented in the form $\mathbb{E}[A_1(\cdot)^\top]\mathbb{E} [Y(\cdot)] $, we cannot solve this optimality system explicitly. To this end, we decompose the MFSLQ control problem into two problems without the mean-field terms, and one of them is a constrained problem. The constrained SLQ control problem is solved explicitly by an extended LaGrange multiplier method developed in this article.

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Jie Xiong, Wen Xu. 2024-06-07. Mean-field stochastic linear quadratic control problem with random coefficients. https://arxiv.org/abs/2406.04621

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