Optimal Execution under Incomplete Information

ArXiv ID: 2411.04616 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: Optimal Liquidation, Hawkes Processes, Limit Order Book (LOB), Hidden Markov Process, Impulse Control, Single Asset (High-Frequency Trading)

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced stochastic calculus, impulse control, stochastic filtering (Kushner-Stratonovich equations), and Markov-modulated Hawkes processes, which is highly mathematically dense. It provides theoretical derivations and numerical simulations but lacks backtested results, real-world data, or specific implementation details for a trading strategy.

  flowchart TD
    A["Research Goal: Find Optimal Liquidation Strategy"] --> B["Model & Methodology"]
    B --> C{"Data: Order Flow, LOB"}
    C --> D["Computational Process: Filtering & Impulse Control"]
    D --> E["Findings: Algorithm & Optimal Strategy"]
    E --> F["Validation: Numerical Results"]