# American Institute of Mathematical Sciences

September  2019, 9(3): 495-507. doi: 10.3934/mcrf.2019022

## A stochastic maximum principle for linear quadratic problem with nonconvex control domain

 Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, Shandong, 250100, China

* Corresponding author: Xiaole Xue

Received  June 2017 Revised  June 2018 Published  April 2019

Fund Project: Research supported by NSF (Nos. 11571203, 11871458).

This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of the proposed maximum principle is illustrated through a work-out example.

Citation: Shaolin Ji, Xiaole Xue. A stochastic maximum principle for linear quadratic problem with nonconvex control domain. Mathematical Control & Related Fields, 2019, 9 (3) : 495-507. doi: 10.3934/mcrf.2019022
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