SIAM Journal on Control and Optimization, Volume 58, Issue 5, Page 2821-2853, January 2020.
In this paper we study a Markovian two-dimensional bounded-variation stochastic control problem whose state process consists of a diffusive mean-reverting component and of a purely controlled one. The main problem's characteristic lies in the interaction of the two components of the state process: the mean-reversion level of the diffusive component is an affine function of the current value of the purely controlled one. By relying on a combination of techniques from viscosity theory and free-boundary analysis, we provide the structure of the value function and we show that it satisfies a second-order smooth-fit principle. Such a regularity is then exploited in order to determine a system of functional equations solved by the two monotone continuous curves (free boundaries) that split the control problem's state space into three connected regions. Further properties of the free boundaries are also obtained.

中文翻译：

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具有相互联系的动力学的奇异随机控制问题

SIAM控制与优化杂志，第58卷，第5期，第2821-2853页，2020年1月。
在本文中，我们研究了一个马尔可夫二维有界变化随机控制问题，该问题的状态过程由扩散均值回复分量和纯受控分量组成。主要问题的特征在于状态过程的两个分量之间的相互作用：扩散分量的均值回复水平是纯受控分量的当前值的仿射函数。通过依赖于粘度理论和自由边界分析技术的结合，我们提供了价值函数的结构，并证明它满足二阶平滑拟合原理。然后利用这种规律性来确定由两个将控制问题分开的单调连续曲线（自由边界）求解的功能方程组。的状态空间分为三个相连的区域。还获得了自由边界的其他性质。