一个带有交易成本的最优投资问题的谱方法（潜在效用下）
A spectral method for an Optimal Investment problem with Transaction Costs under Potential Utility
AI总结：
本文提出了一种谱方法，用于求解带有交易成本的有限时间 horizon 最优投资问题，通过极坐标变换将问题转化为有限域内的单变量问题，提高了数值解的效率。
摘要：
本文关注有限时间 horizon 最优投资问题在潜在效用下的数值解。问题最初以带有梯度约束的演化HJB方程形式提出。在《有限时间 horizon 最优投资与交易成本：一个抛物双障碍问题》中，问题被重新表述为一个非线性抛物双障碍问题，定义在无界域中，并获得了若干显式性质和公式。将问题转换为极坐标允许在有限域内以单变量形式提出问题，从而避免了先前问题数值解的一些技术困难。如果需要高精度，所提出的谱数值方法比有限差分等简单方法更有效。
英文摘要：
This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem, Day-Yi, the problem is reformulated as a non-linear parabolic double obstacle problem posed in one spatial variable and defined in an unbounded domain where several explicit properties and formulas are obtained. The restatement of the problem in polar coordinates allows to pose the problem in one spatial variable in a finite domain, avoiding some of the technical difficulties of the numerical solution of the previous statement of the problem. If high precision is required, the spectral numerical method proposed becomes more efficient than simpler methods as finite differences for example.
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