Global Closed-Form Approximation of Free Boundary for Optimal Investment Stopping Problems
Global Closed-Form Approximation of Free Boundary for Optimal Investment Stopping Problems
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DOI：
10.1137/18m1184850
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发表时间：
2018-10
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影响因子：
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通讯作者：
Jingtang Ma;Jie Xing;Harry Zheng
中科院分区：
文献类型：
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作者：
Jingtang Ma;Jie Xing;Harry Zheng
本文研究了有限时间内具有最优控制和最优停止的效用最大化问题。值函数可以用一个变分方程来描述，该变分方程涉及一个完全非线性偏微分方程的自由边界问题。利用对偶控制方法，我们得到了一类效用函数（包括幂效用函数和非HARA效用函数）的对偶值函数及其对偶自由边界的渐近性质。我们构造了一个全局封闭形式的近似的对偶自由边界，这大大降低了计算成本。利用对偶关系，我们得到了最优投资停止问题的最优价值函数、交易策略和执行边界的近似公式。数值算例表明，该方法具有鲁棒性好、精度高、速度快的特点。
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a fully nonlinear partial differential equation. Using the dual control method, we derive the asymptotic properties of the dual value function and the associated dual free boundary for a class of utility functions, including power and non-HARA utilities. We construct a global closed-form approximation to the dual free boundary, which greatly reduces the computational cost. Using the duality relation, we find the approximate formulas for the optimal value function, trading strategy, and exercise boundary for the optimal investment stopping problem. Numerical examples show the approximation is robust, accurate and fast.