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Nash equilibrium for risk-averse investors in a market impact game with transient price impact

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  • Xiangge Luo
  • Alexander Schied

Abstract

We consider a market impact game for $n$ risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finite and infinite time horizons, the agents aim to minimize a mean-variance functional of their costs or to maximize the expected exponential utility of their revenues. We give explicit representations for corresponding Nash equilibria and prove uniqueness in the case of mean-variance optimization. A qualitative analysis of these Nash equilibria is conducted by means of numerical analysis.

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  • 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.
    • Handle: RePEc:arx:papers:1807.03813
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    References listed on IDEAS

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    1. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    2. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    3. 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.
    4. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    5. Julian Lorenz & Robert Almgren, 2011. "Mean--Variance Optimal Adaptive Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(5), pages 395-422, January.
    6. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    7. Fouque,Jean-Pierre & Langsam,Joseph A. (ed.), 2013. "Handbook on Systemic Risk," Cambridge Books, Cambridge University Press, number 9781107023437.
    8. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    9. 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.
    10. 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.
    11. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
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    Cited by:

    1. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "Portfolio liquidation games with self‐exciting order flow," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1020-1065, October.
    2. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    3. Moritz Voß, 2022. "A two-player portfolio tracking game," Mathematics and Financial Economics, Springer, volume 16, number 6, June.

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