IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v178y2024ics0304414924001674.html
   My bibliography  Save this article

A mean field game approach to equilibrium consumption under external habit formation

Author

Listed:
  • Bo, Lijun
  • Wang, Shihua
  • Yu, Xiang

Abstract

This paper studies the equilibrium consumption under external habit formation in a large population of agents. We first formulate problems under two types of conventional habit formation preferences, namely linear and multiplicative external habit formation, in a mean field game framework. In a log-normal market model with the asset specialization, we characterize one mean field equilibrium in analytical form in each problem, allowing us to understand some quantitative properties of the equilibrium strategy and conclude some financial implications caused by consumption habits from a mean-field perspective. In each problem with n agents, we construct an approximate Nash equilibrium for the n-player game using the obtained mean field equilibrium when n is sufficiently large. The explicit convergence order in each problem can also be obtained.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001674
    DOI: 10.1016/j.spa.2024.104461
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924001674
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2024.104461?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. Shuoqing Deng & Xun Li & Huyên Pham & Xiang Yu, 2022. "Optimal consumption with reference to past spending maximum," Finance and Stochastics, Springer, vol. 26(2), pages 217-266, April.
    3. van Bilsen, Servaas & Bovenberg, A. Lans & Laeven, Roger J. A., 2020. "Consumption and Portfolio Choice under Internal Multiplicative Habit Formation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(7), pages 2334-2371, November.
    4. 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.
    5. 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.
    6. Shuoqing Deng & Xun Li & Huyên Pham & Xiang Yu, 2022. "Optimal consumption with reference to past spending maximum," Post-Print hal-03947571, HAL.
    7. Guanxing Fu & Chao Zhou, 2023. "Mean field portfolio games," Finance and Stochastics, Springer, vol. 27(1), pages 189-231, January.
    8. Mark Schroder & Costis Skiadas, 2002. "An Isomorphism Between Asset Pricing Models With and Without Linear Habit Formation," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1189-1221.
    9. Xiang Yu, 2011. "Utility maximization with addictive consumption habit formation in incomplete semimartingale markets," Papers 1112.2940, arXiv.org, revised May 2015.
    10. 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.
    11. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, February.
    12. Xun Li & Xiang Yu & Qinyi Zhang, 2021. "Optimal consumption with loss aversion and reference to past spending maximum," Papers 2108.02648, arXiv.org, revised Mar 2024.
    13. Jerome B. Detemple & Fernando Zapatero, 1992. "Optimal Consumption‐Portfolio Policies With Habit Formation1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 251-274, October.
    14. 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.
    15. 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.
    16. Shuoqing Deng & Xun Li & Huyen Pham & Xiang Yu, 2020. "Optimal Consumption with Reference to Past Spending Maximum," Papers 2006.07223, arXiv.org, revised Mar 2022.
    17. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    18. 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.
    19. Carroll, Christopher D., 2000. "Solving consumption models with multiplicative habits," Economics Letters, Elsevier, vol. 68(1), pages 67-77, July.
    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. 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.
    2. Li, Xun & Yu, Xiang & Zhang, Qinyi, 2023. "Optimal consumption and life insurance under shortfall aversion and a drawdown constraint," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 25-45.
    3. 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.
    4. Johdo, Wataru, 2009. "Habit persistence and stagnation," Economic Modelling, Elsevier, vol. 26(5), pages 1110-1114, September.
    5. Xun Li & Xiang Yu & Qinyi Zhang, 2021. "Optimal consumption with loss aversion and reference to past spending maximum," Papers 2108.02648, arXiv.org, revised Mar 2024.
    6. Zongxia Liang & Keyu Zhang, 2024. "A Mean Field Game Approach to Relative Investment-Consumption Games with Habit Formation," Papers 2401.15659, arXiv.org.
    7. Kakeu, Johnson & Nguimkeu, Pierre, 2017. "Habit formation and exhaustible resource risk-pricing," Energy Economics, Elsevier, vol. 64(C), pages 1-12.
    8. Roman Muraviev, 2011. "Additive habits with power utility: Estimates, asymptotics and equilibrium," Papers 1108.2889, arXiv.org.
    9. Xiang Yu, 2014. "Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments," Papers 1408.1382, arXiv.org, revised Jul 2016.
    10. 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).
    11. Geonwoo Kim & Junkee Jeon, 2024. "Dynamic Asset Allocation and Retirement Decision with Consumption Ratcheting and Effort Choice," Mathematics, MDPI, vol. 12(23), pages 1-18, December.
    12. Leroux, Anke D. & Martin, Vance L. & Zheng, Hao, 2018. "Addressing water shortages by force of habit," Resource and Energy Economics, Elsevier, vol. 53(C), pages 42-61.
    13. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    14. Kraft, Holger & Meyer-Wehmann, André & Seifried, Frank Thomas, 2022. "Endogenous habits and equilibrium asset prices," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 279-300.
    15. Guohui Guan & Qitao Huang & Zongxia Liang & Fengyi Yuan, 2020. "Retirement decision with addictive habit persistence in a jump diffusion market," Papers 2011.10166, arXiv.org, revised Feb 2024.
    16. Kris Jacobs, 2001. "Estimating Nonseparable Preference Specifications for Asset Market Participants," CIRANO Working Papers 2001s-12, CIRANO.
    17. Emilio Fernandez-Corugedo, 2004. "Consumption Theory," Handbooks, Centre for Central Banking Studies, Bank of England, number 23, April.
    18. Santiago Budría, 2008. "An Exploration of Asset Returns in a Production Economy with Relative Habits," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 36(3), pages 261-274, September.
    19. Smith, William T. & Zhang, Qiang, 2007. "Asset pricing with multiplicative habit and power-expo preferences," Economics Letters, Elsevier, vol. 94(3), pages 319-325, March.
    20. Longstaff, Francis A. & Piazzesi, Monika, 2004. "Corporate earnings and the equity premium," Journal of Financial Economics, Elsevier, vol. 74(3), pages 401-421, December.

    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:eee:spapps:v:178:y:2024:i:c:s0304414924001674. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.