Trade execution games in a Markovian environment

ArXiv ID: 2405.07184 “View on arXiv”

Authors: Unknown

Abstract

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders’ execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class; it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets.

Keywords: optimal execution, market impact, stochastic control, Markov games, game theory

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is highly mathematically dense, featuring Markov game theory, dynamic programming, backward induction, and closed-form equilibrium solutions, yet it relies solely on simulation-based experiments with no real data, backtests, or implementation details.

  flowchart TD
    A["Research Goal: Find Optimal Trade Execution<br>Strategy in Stochastic Market"] --> B["Modeling Framework"]
    
    B --> C["Markov Game Model<br>Two Large Traders + Stochastic Environment"]
    
    C --> D{"Data Inputs"}
    D --> E["Market Price Dynamics<br>Generalized Impact Parameters"]
    D --> F["Utility Preferences<br>Risk Aversion Factors"]
    
    E & F --> G["Computational Process<br>Backward Induction & Dynamic Programming"]
    
    G --> H{"Key Findings"}
    H --> I["Closed-Form Solution<br>Markov Perfect Equilibrium"]
    H --> J["Deterministic Strategy<br>(Stochastic Environment)"]/Deterministic Strategy<br>when Environment is Deterministic