IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v18y2024i4d10.1007_s11579-024-00360-4.html
   My bibliography  Save this book

A mean field game approach to relative investment–consumption games with habit formation

Author

Listed:
  • Zongxia Liang

    (Tsinghua University)

  • Keyu Zhang

    (Tsinghua University)

Abstract

This paper studies an optimal investment–consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as benchmarks to evaluate the performance of her decision. We formulate the n-agent game problems and the corresponding mean field game problems under the two utilities. One mean field equilibrium is derived in a closed form in each problem. In each problem with n agents, an approximate Nash equilibrium is then constructed using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained. In addition, we provide some numerical illustrations of our results.

Suggested Citation

  • Zongxia Liang & Keyu Zhang, 2024. "A mean field game approach to relative investment–consumption games with habit formation," Mathematics and Financial Economics, Springer, volume 18, number 2, February.
    • Handle: RePEc:spr:mathfi:v:18:y:2024:i:4:d:10.1007_s11579-024-00360-4
    DOI: 10.1007/s11579-024-00360-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-024-00360-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11579-024-00360-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Abel, Andrew B, 1990. "Asset Prices under Habit Formation and Catching Up with the Joneses," American Economic Review, American Economic Association, vol. 80(2), pages 38-42, May.
    2. Jesus Fernández-Villaverde & Dirk Krueger, 2007. "Consumption over the Life Cycle: Facts from Consumer Expenditure Survey Data," The Review of Economics and Statistics, MIT Press, vol. 89(3), pages 552-565, August.
    3. Jana Bielagk & Arnaud Lionnet & Goncalo Dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Papers 1511.04218, arXiv.org, revised Feb 2017.
    4. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    5. Vayanos, Dimitri, 1998. "Transaction Costs and Asset Prices: A Dynamic Equilibrium Model," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 1-58.
    6. Thurow, Lester C, 1969. "The Optimum Lifetime Distribution of Consumption Expenditures," American Economic Review, American Economic Association, vol. 59(3), pages 324-330, June.
    7. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    8. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    9. Guanxing Fu & Chao Zhou, 2023. "Mean field portfolio games," Finance and Stochastics, Springer, vol. 27(1), pages 189-231, January.
    10. Detemple, Jerome B & Zapatero, Fernando, 1991. "Asset Prices in an Exchange Economy with Habit Formation," Econometrica, Econometric Society, vol. 59(6), pages 1633-1657, November.
    11. 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.
    12. 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.
    13. Yushi Hamaguchi, 2019. "Time-inconsistent consumption-investment problems in incomplete markets under general discount functions," Papers 1912.01281, arXiv.org, revised Mar 2021.
    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. Zongxia Liang & Keyu Zhang, 2024. "A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation," Papers 2401.15659, arXiv.org.
    2. Bo, Lijun & Wang, Shihua & Yu, Xiang, 2024. "A mean field game approach to equilibrium consumption under external habit formation," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    3. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. Choi, Kyoung Jin & Jeon, Junkee & Koo, Hyeng Keun, 2022. "Intertemporal preference with loss aversion: Consumption and risk-attitude," Journal of Economic Theory, Elsevier, vol. 200(C).
    5. Holger Kraft & Claus Munk & Frank Thomas Seifried & Sebastian Wagner, 2017. "Consumption habits and humps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 305-330, August.
    6. Francisco Gomes & Alexander Michaelides, 2003. "Portfolio Choice With Internal Habit Formation: A Life-Cycle Model With Uninsurable Labor Income Risk," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 729-766, October.
    7. Holger Kraft & Claus Munk & Sebastian Wagner, 2018. "Housing Habits and Their Implications for Life-Cycle Consumption and Investment [The evolution of homeownership rates in selected OECD countries: demographic and public policy influences]," Review of Finance, European Finance Association, vol. 22(5), pages 1737-1762.
    8. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    9. 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.
    10. Kris Jacobs, 2001. "Estimating Nonseparable Preference Specifications for Asset Market Participants," CIRANO Working Papers 2001s-12, CIRANO.
    11. Hlouskova, Jaroslava & Fortin, Ines & Tsigaris, Panagiotis, 2019. "The consumption–investment decision of a prospect theory household: A two-period model with an endogenous second period reference level," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 93-108.
    12. Kihlstrom, Richard, 2009. "Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 634-663, September.
    13. Matsen, Egil, 2003. "Habit persistence and welfare gains from international asset trade," Journal of International Money and Finance, Elsevier, vol. 22(2), pages 239-260, April.
    14. Carolina Achury & Sylwia Hubar & Christos Koulovatianos, 2012. "Saving Rates and Portfolio Choice with Subsistence Consumption," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 108-126, January.
    15. Longstaff, Francis A. & Piazzesi, Monika, 2004. "Corporate earnings and the equity premium," Journal of Financial Economics, Elsevier, vol. 74(3), pages 401-421, December.
    16. Eduard Dubin & Olesya V. Grishchenko & Vasily Kartashov, 2012. "Habit formation heterogeneity: Implications for aggregate asset pricing," Finance and Economics Discussion Series 2012-07, Board of Governors of the Federal Reserve System (U.S.).
    17. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    18. Jacobs, Kris, 2000. "Estimating Nonseparable Preference Specifications for Asset Market Participants," Econometric Society World Congress 2000 Contributed Papers 1472, Econometric Society.
    19. Kris Jacobs, 2002. "The Rate of Risk Aversion May Be Lower Than You Think," CIRANO Working Papers 2002s-08, CIRANO.
    20. Qiang Dai & Olesya V. Grishchenko, 2014. "An Empirical Investigation of Consumption-Based Asset Pricing Models with Stochastic Habit Formation," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-34.

    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:spr:mathfi:v:18:y:2024:i:4:d:10.1007_s11579-024-00360-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.