英文标题：
《Global Closed-form Approximation of Free Boundary for Optimal Investment
Stopping Problems》
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作者：
Jingtang Ma, Jie Xing, Harry Zheng
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最新提交年份：
2018
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英文摘要：
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.
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中文摘要：
本文研究有限时间范围内同时具有最优控制和最优停止的效用最大化问题。该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。我们构造了对偶自由边界的全局闭式近似，大大降低了计算量。利用对偶关系，我们找到了最优投资停止问题的最优值函数、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、速度快等优点。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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