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Mean field games with unbounded controlled common noise in portfolio management with relative performance criteria

Author

Listed:
  • Panagiotis E. Souganidis

    (The University of Texas at Austin, Departments of Mathematics and IROM, and the Oxford-Man Institute of Quantitative Finance, University of Oxford)

  • Thaleia Zariphopoulou

    (University of Chicago)

Abstract

Motivated by optimal allocation models with relative performance criteria, we introduce a mean field game in which the terminal expected utility of the representative agent depends on her own state as well as the average of her peers. We derive the master equation, which, in view of the presence of controls in the volatility, needs to be coupled with a compatibility condition for the mean field optimal feedback control. We concentrate on the class of separable payoffs under both general utilities and couplings. We derive a solution to the master equation and find the associated optimal feedback control expressed via the value function in the absence of competition and a dynamic coupling function solving a non-local quasilinear equation. In turn, we construct the related optimal state and control processes, and give representative examples. Projecting the mean field solutions on finite dimensions, we recover the solution of the N-game for linear couplings and arbitrary utilities, and we study the proximity of these approximations to their N-player game counterparts.

Suggested Citation

  • Panagiotis E. Souganidis & Thaleia Zariphopoulou, 2024. "Mean field games with unbounded controlled common noise in portfolio management with relative performance criteria," Mathematics and Financial Economics, Springer, volume 18, number 10, December.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:2:d:10.1007_s11579-024-00363-1
    DOI: 10.1007/s11579-024-00363-1
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    References listed on IDEAS

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    1. Phelim Boyle & Lorenzo Garlappi & Raman Uppal & Tan Wang, 2012. "Keynes Meets Markowitz: The Trade-Off Between Familiarity and Diversification," Management Science, INFORMS, vol. 58(2), pages 253-272, February.
    2. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    3. repec:bla:jfinan:v:53:y:1998:i:5:p:1589-1622 is not listed on IDEAS
    4. Suleyman Basak & Dmitry Makarov, 2014. "Strategic Asset Allocation in Money Management," Journal of Finance, American Finance Association, vol. 69(1), pages 179-217, February.
    5. Alexander Kempf & Stefan Ruenzi, 2008. "Tournaments in Mutual-Fund Families," The Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 1013-1036, April.
    6. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    7. Peter M. DeMarzo & Ron Kaniel & Ilan Kremer, 2008. "Relative Wealth Concerns and Financial Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 19-50, January.
    8. Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    9. Nicole Bäuerle & Tamara Göll, 2023. "Nash equilibria for relative investors via no-arbitrage arguments," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 1-23, February.
    10. Stephen J. Brown & William N. Goetzmann & James Park, 2001. "Careers and Survival: Competition and Risk in the Hedge Fund and CTA Industry," Journal of Finance, American Finance Association, vol. 56(5), pages 1869-1886, October.
    11. Nicole Bauerle & Tamara Goll, 2023. "Nash equilibria for relative investors with (non)linear price impact," Papers 2303.18161, arXiv.org, revised Apr 2024.
    12. Lijun Bo & Shihua Wang & Xiang Yu, 2022. "A mean field game approach to equilibrium consumption under external habit formation," Papers 2206.13341, arXiv.org, revised Mar 2024.
    13. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    14. Anastasiya Tanana, 2023. "Relative performance criteria of multiplicative form in complete markets," Papers 2303.07941, arXiv.org.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. Todd Mitton & Keith Vorkink, 2007. "Equilibrium Underdiversification and the Preference for Skewness," The Review of Financial Studies, Society for Financial Studies, vol. 20(4), pages 1255-1288.
    17. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, September.
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