A STOCHASTIC CONTROL PROBLEM AND RELATED FREE BOUNDARIES IN FINANCE
A STOCHASTIC CONTROL PROBLEM AND RELATED FREE BOUNDARIES IN FINANCE
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金融中的随机控制问题和相关自由边界
DOI：
10.3934/mcrf.2017021
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发表时间：
2017
影响因子：
1.2
通讯作者：
Yi Fahuai
中科院分区：
文献类型：
--
作者：
Guan Chonghu;Li Xun;Xu Zuo Quan;Yi Fahuai
在本文中，我们研究了一个最优停止问题（混合随机控制）的经理，其效用是非光滑和非凹在有限的时间范围内。本文的目的是发展一种新的方法，这是显着不同的混合动态最优控制和停止问题在现有文献中，以找出管理者的最佳策略。该问题首先转化为一个完全非线性算子的自由边界问题。然后，通过对偶变换，将其转化为带有线性算子的自由边值问题，从而可以用经典方法求解。最后，利用逆变换，我们得到了原问题的最优交易策略和最优停时的性质。
In this paper, we investigate an optimal stopping problem (mixed with stochastic controls) for a manager whose utility is nonsmooth and nonconcave over a finite time horizon. The paper aims to develop a new methodology, which is significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, so as to figure out the manager's best strategies. The problem is first reformulated into a free boundary problem with a fully nonlinear operator. Then, by means of a dual transformation, it is further converted into a free boundary problem with a linear operator, which can be consequently tackled by the classical method. Finally, using the inverse transformation, we obtain the properties of the optimal trading strategy and the optimal stopping time for the original problem.