标题： 在不完全信息下的最优执行 显示英文标题

标题： Optimal Execution under Incomplete Information

摘要： 我们研究在部分信息下针对单一资产的有限时间范围内的最优清算策略。 我们提出一个专为高频交易设计的模型，通过相互刺激的标记霍克斯过程捕捉仅由订单流驱动的价格形成。 该模型假设一个限价订单簿框架，考虑了永久性价格影响和瞬时市场影响。 重要的是，我们将流动性作为隐藏的马尔可夫过程，影响决定买卖价格点过程强度。 在此背景下，我们将最优清算问题表述为脉冲控制问题。 我们阐明了隐藏马尔可夫链滤波器的动力学，并确定了相关的归一化滤波方程。 然后，我们将价值函数表示为一系列辅助连续函数的极限，这些函数是递归定义的。 这种表征使得可以使用动态规划原理来解决最优停止问题并确定最优策略。 它还促进了可实现算法的开发，以近似原始清算问题。 我们通过数值结果和候选最优策略的可视化来丰富我们的分析。 显示英文摘要

摘要： We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through mutually stimulating marked Hawkes processes. The model assumes a limit order book framework, accounting for both permanent price impact and transient market impact. Importantly, we incorporate liquidity as a hidden Markov process, influencing the intensities of the point processes governing bid and ask prices. Within this setting, we formulate the optimal liquidation problem as an impulse control problem. We elucidate the dynamics of the hidden Markov chain's filter and determine the related normalized filtering equations. We then express the value function as the limit of a sequence of auxiliary continuous functions, defined recursively. This characterization enables the use of a dynamic programming principle for optimal stopping problems and the determination of an optimal strategy. It also facilitates the development of an implementable algorithm to approximate the original liquidation problem. We enrich our analysis with numerical results and visualizations of candidate optimal strategies.