Paper: arXiv 2405.07184

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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

Cited References (43)

  1. Optimal Execution with Dynamic Order Flow Imbalance (2015) — link
  2. VOLATILITY AND COVARIATION ESTIMATION WHEN MICROSTRUCTURE NOISE AND TRADING TIMES ARE ENDOGENOUS (2010) — link
  3. Optimal execution of portfolio transactions (2001) — link
  4. Optimal control of execution costs (1998) — link
  5. Zero-intelligence realized variance estimation (2010) — link
  6. Optimal Trading Strategy and Supply/Demand Dynamics (2005) — link
  7. Continuous Auctions and Insider Trading (1985) — link
  8. Optimal Execution in Illiquid Market with the Absence of Price Manipulation (2015) — link
and 35 more
  1. No-dynamic-arbitrage and market impact (2010) — link
  2. More Statistical Properties of Order Books and Price Impact (2004) — link
  3. Fluctuations and Response in Financial Markets: The Subtle Nature of ‘Random’ Price Changes (2004) — link
  4. Algorithmic and High Frequency Trading (2016) — link
  5. Dynamic portfolio choice with frictions (2016) — link
  6. Trade execution in illiquid markets: Optimal stochastic control and multi-agent equilibria (2008) — link
  7. Optimal Off-Exchange Execution with Closing Price (2017) — link
  8. Incorporating signals into optimal trading (2019) — link
  9. Nash Equilibrium for Risk-Averse Investors in a Market Impact Game with Transient Price Impact (2019) — link
  10. Mean‐field games with differing beliefs for algorithmic trading (2020) — link
  11. Trading co‐integrated assets with price impact (2018) — link
  12. Optimal and Equilibrium Execution Strategies with Generalized Price Impact (2019) — link
  13. The Price Impact of Order Book Events (2013) — link
  14. A Market Impact Game Under Transient Price Impact (2018) — link
  15. The Flash Crash: High‐Frequency Trading in an Electronic Market (2017) — link
  16. Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact (2022) — link
  17. Instabilities in multi-asset and multi-agent market impact games (2022) — link
  18. Optimal trading strategy and supply/demand dynamics (2012) — link
  19. Nash equilibrium for risk-averse investors in a market impact game with transient price impact (2018) — link
  20. More statistical properties of order books and price impact (2003) — link
  21. Statistical Arbitrage in the U.S. Equities Market (2008) — link
  22. The micro-price: a high-frequency estimator of future prices (2018) — link
  23. Optimal Trading with Signals and Stochastic Price Impact (2022) — link
  24. Enhancing trading strategies with order book signals (2018) — link
  25. ALGORITHMIC TRADING WITH LEARNING (2016) — link
  26. Mean-Field Game Strategies for Optimal Execution (2019) — link
  27. A Closed-Form Execution Strategy to Target Volume Weighted Average Price (2016) — link
  28. Dynamic Trading with Predictable Returns and Transaction Costs (2013) — link
  29. Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes (2004) — link
  30. Incorporating order-flow into optimal execution (2016) — link
  31. Optimal trade execution for Gaussian signals with power-law resilience (2021) — link
  32. DISCRETE-TIME OPTIMAL EXECUTION UNDER A GENERALIZED PRICE IMPACT MODEL WITH MARKOVIAN EXOGENOUS ORDERS (2020) — link
  33. Optimal Pair–Trade Execution with Generalized Cross–Impact (2021) — link
  34. The Financial Mathematics of Market Liquidity (2016) — link
  35. Introduction to Optimal Execution (2024) — link

0 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.