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A two-player portfolio tracking game

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Listed:
  • Moritz Voß

    (University of California Los Angeles)

Abstract

We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank et al. (Math Financial Economics 11(2):215–239 2017). Specifically, both agents track their own stochastic running trading targets while interacting through common aggregated temporary and permanent price impact à la Almgren and Chriss (J Risk 3:5–39 2001). The resulting stochastic linear quadratic differential game with terminal state constraints allows for a unique and explicitly available open-loop Nash equilibrium. Our results reveal how the equilibrium strategies of the two players take into account the other agent’s trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the relation between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement and extend existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation games.

Suggested Citation

  • Moritz Voß, 2022. "A two-player portfolio tracking game," Mathematics and Financial Economics, Springer, volume 16, number 6, December.
    • Handle: RePEc:spr:mathfi:v:16:y:2022:i:4:d:10.1007_s11579-022-00324-6
    DOI: 10.1007/s11579-022-00324-6
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    References listed on IDEAS

    as
    1. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    2. Alexander Schied & Tao Zhang, 2019. "A Market Impact Game Under Transient Price Impact," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 102-121, February.
    3. Ibrahim Ekren & Sergey Nadtochiy, 2022. "Utility‐based pricing and hedging of contingent claims in Almgren‐Chriss model with temporary price impact," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 172-225, January.
    4. Alexander Schied & Elias Strehle & Tao Zhang, 2015. "High-frequency limit of Nash equilibria in a market impact game with transient price impact," Papers 1509.08281, arXiv.org, revised May 2017.
    5. Xiangge Luo & Alexander Schied, 2018. "Nash equilibrium for risk-averse investors in a market impact game with transient price impact," Papers 1807.03813, arXiv.org, revised Jun 2019.
    6. Philippe Casgrain & Sebastian Jaimungal, 2020. "Mean‐field games with differing beliefs for algorithmic trading," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 995-1034, July.
    7. Mukarram Attari & Antonio S. Mello & Martin E. Ruckes, 2005. "Arbitraging Arbitrageurs," Journal of Finance, American Finance Association, vol. 60(5), pages 2471-2511, October.
    8. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
    9. Alexander Schied & Tao Zhang, 2017. "A State-Constrained Differential Game Arising In Optimal Portfolio Liquidation," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 779-802, July.
    10. Chenghuan Sean Chu & Andreas Lehnert & Wayne Passmore, 2009. "Strategic Trading in Multiple Assets and the Effects on Market Volatiliy," International Journal of Central Banking, International Journal of Central Banking, vol. 5(4), pages 143-172, December.
    11. Xuancheng Huang & Sebastian Jaimungal & Mojtaba Nourian, 2019. "Mean-Field Game Strategies for Optimal Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(2), pages 153-185, March.
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    More about this item

    Keywords

    Stochastic differential game; Nash equilibrium; Illiquid markets; Portfolio tracking; Predatory trading;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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