SIAM Journal on Financial Mathematics, Volume 12, Issue 2, Page 788-822, January 2021.
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions and at discrete points in time. We derive an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs. We also discuss several qualitative aspects of optimal strategies, such as existence of profitable round trips or closing the position in one go, and compare our findings with the literature.

中文翻译：

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具有随机流动性参数的订单簿模型中的最优交易执行

SIAM Journal on Financial Mathematics，第 12 卷，第 2 期，第 788-822 页，2021 年 1 月。
我们分析了具有随机流动性的金融市场中的最优交易执行问题。为此，我们建立了一个限价订单簿模型，其中订单簿深度和弹性随时间随机变化。允许在两个方向和离散时间点进行交易。我们推导出一个显式递归，在某些结构假设下，它具有最小执行成本的特征。我们还讨论了最佳策略的几个定性方面，例如是否存在有利可图的往返或一次性平仓，并将我们的发现与文献进行比较。