IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1703.07685.html
   My bibliography  Save this paper

Mean field and n-agent games for optimal investment under relative performance criteria

Author

Listed:
  • Daniel Lacker
  • Thaleia Zariphopoulou

Abstract

We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log-normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mean field games, which we show are unique in the class of constant equilibria. In the CARA case, competition drives agents to invest more in the risky asset than they would otherwise, while in the CRRA case competitive agents may over- or under-invest, depending on their levels of risk tolerance.

Suggested Citation

  • Daniel Lacker & Thaleia Zariphopoulou, 2017. "Mean field and n-agent games for optimal investment under relative performance criteria," Papers 1703.07685, arXiv.org, revised Jun 2018.
    • Handle: RePEc:arx:papers:1703.07685
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1703.07685
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    3. Raman Uppal & Tan Wang, 2003. "Model Misspecification and Underdiversification," Journal of Finance, American Finance Association, vol. 58(6), pages 2465-2486, December.
    4. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    5. Robert E. Lucas Jr. & Benjamin Moll, 2014. "Knowledge Growth and the Allocation of Time," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 1-51.
    6. Joshua D. Coval & Tobias J. Moskowitz, 1999. "Home Bias at Home: Local Equity Preference in Domestic Portfolios," Journal of Finance, American Finance Association, vol. 54(6), pages 2045-2073, December.
    7. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    8. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    9. Suleyman Basak & Dmitry Makarov, 2013. "Competition among Portfolio Managers and Asset Specialization," Working Papers w0194, Center for Economic and Financial Research (CEFIR).
    10. Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
    11. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    12. Stijn Van Nieuwerburgh & Laura Veldkamp, 2009. "Information Immobility and the Home Bias Puzzle," Journal of Finance, American Finance Association, vol. 64(3), pages 1187-1215, June.
    13. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
    14. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    15. 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.
    16. repec:bla:jfinan:v:53:y:1998:i:5:p:1589-1622 is not listed on IDEAS
    17. 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.
    18. 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.
    19. Marcin Kacperczyk & Clemens Sialm & Lu Zheng, 2005. "On the Industry Concentration of Actively Managed Equity Mutual Funds," Journal of Finance, American Finance Association, vol. 60(4), pages 1983-2011, August.
    20. Brennan, M. J., 1975. "The Optimal Number of Securities in a Risky Asset Portfolio When There Are Fixed Costs of Transacting: Theory and Some Empirical Results," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(3), pages 483-496, September.
    21. Liu, Hong, 2014. "Solvency Constraint, Underdiversification, and Idiosyncratic Risks," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(2), pages 409-430, April.
    22. 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.
    23. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    24. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Suleyman Basak & Dmitry Makarov, 2013. "Competition among Portfolio Managers and Asset Specialization," Working Papers w0194, New Economic School (NES).
    2. Michail Anthropelos & Tianran Geng & Thaleia Zariphopoulou, 2020. "Competition in Fund Management and Forward Relative Performance Criteria," Papers 2011.00838, arXiv.org.
    3. Guiso, Luigi & Sodini, Paolo, 2013. "Household Finance: An Emerging Field," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1397-1532, Elsevier.
    4. Gu Wang & Jiaxuan Ye, 2023. "Fund Managers’ Competition for Investment Flows Based on Relative Performance," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 605-643, August.
    5. 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.
    6. Mark Whitmeyer, 2019. "Relative performance concerns among investment managers," Annals of Finance, Springer, vol. 15(2), pages 205-231, June.
    7. 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, March.
    8. 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.
    9. Hui Chen & Nengjiu Ju & Jianjun Miao, 2014. "Dynamic Asset Allocation with Ambiguous Return Predictability," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(4), pages 799-823, October.
    10. Jiang, Julia & Liu, Jun & Tian, Weidong & Zeng, Xudong, 2022. "Portfolio concentration, portfolio inertia, and ambiguous correlation," Journal of Economic Theory, Elsevier, vol. 203(C).
    11. Lin, Qian & Luo, Yulei & Sun, Xianming, 2022. "Robust investment strategies with two risky assets," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    12. Giannetti, Mariassunta & Laeven, Luc, 2012. "Local Bias and Stock Market Conditions," CEPR Discussion Papers 8969, C.E.P.R. Discussion Papers.
    13. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    14. Jagannathan, Murali & Jiao, Wei & Karolyi, G. Andrew, 2022. "Is there a home field advantage in global markets?," Journal of Financial Economics, Elsevier, vol. 143(2), pages 742-770.
    15. Tao Shu & Johan Sulaeman & P. Eric Yeung, 2012. "Local Religious Beliefs and Mutual Fund Risk-Taking Behaviors," Management Science, INFORMS, vol. 58(10), pages 1779-1796, October.
    16. Chen, XiaoHua & Lai, Yun-Ju, 2015. "On the concentration of mutual fund portfolio holdings: Evidence from Taiwan," Research in International Business and Finance, Elsevier, vol. 33(C), pages 268-286.
    17. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    18. Wang, Ning & Zhang, Yumo, 2024. "Robust asset-liability management games for n players under multivariate stochastic covariance models," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 67-98.
    19. Massa, Massimo & Bai, Jennie, 2021. "Is Hard and Soft Information Substitutable? Evidence from the Lockdowns," CEPR Discussion Papers 15744, C.E.P.R. Discussion Papers.
    20. Andrew Papanicolaou, 2018. "Backward SDEs for Control with Partial Information," Papers 1807.08222, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1703.07685. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.