Abstract In this article, we consider an optimal execution problem with fixed time horizon and bounded transaction rate, which is more natural in practice. We show that, different from traditional stochastic control or singular control problems, this problem is of the stochastic bang-bang control type. Under some parameter settings we show that the optimal control does not involve buy action, and the optimal value function is the viscosity solution to the associated Hamilton-Jacobi-Bellman equation. We further show that the optimal policy is unique, and provide a numerical example to explore the form of the optimal control.

中文翻译：

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有界交易率的有限范围最优执行

摘要 在本文中，我们考虑了一个具有固定时间范围和有界交易率的最优执行问题，这在实践中更自然。我们表明，与传统的随机控制或奇异控制问题不同，该问题属于随机 bang-bang 控制类型。在一些参数设置下，我们表明最优控制不涉及购买行为，最优值函数是相关的 Hamilton-Jacobi-Bellman 方程的粘度解。我们进一步证明了最优策略是唯一的，并提供了一个数值例子来探索最优控制的形式。