IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2106.06185.html
   My bibliography  Save this paper

Mean Field Portfolio Games

Author

Listed:
  • Guanxing Fu
  • Chao Zhou

Abstract

We study mean field portfolio games with random market parameters, where each player is concerned with not only her own wealth but also relative performance to her competitors. We use the martingale optimality principle approach to characterize the unique Nash equilibrium in terms of a mean field FBSDE with quadratic growth, which is solvable under a weak interaction assumption. Motivated by the weak interaction assumption, we establish an asymptotic expansion result in powers of the competition parameter. When the market parameters do not depend on the Brownian paths, we obtain the Nash equilibrium in closed form.

Suggested Citation

  • Guanxing Fu & Chao Zhou, 2021. "Mean Field Portfolio Games," Papers 2106.06185, arXiv.org, revised Apr 2022.
    • Handle: RePEc:arx:papers:2106.06185
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2106.06185
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    2. Martin Herdegen & Johannes Muhle-Karbe & Dylan Possamai, 2019. "Equilibrium Asset Pricing with Transaction Costs," Papers 1901.10989, arXiv.org, revised Sep 2020.
    3. Ruimeng Hu & Thaleia Zariphopoulou, 2021. "$N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction," Papers 2106.00581, arXiv.org, revised Jun 2021.
    4. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
    5. 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.
    6. Briand, Philippe & Confortola, Fulvia, 2008. "BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 818-838, May.
    7. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    8. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    9. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    10. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zongxia Liang & Keyu Zhang, 2023. "Time-inconsistent mean field and n-agent games under relative performance criteria," Papers 2312.14437, arXiv.org, revised Apr 2024.
    2. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.
    3. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, December.
    4. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," CARF F-Series CARF-F-559, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Bo, Lijun & Wang, Shihua & Zhou, Chao, 2024. "A mean field game approach to optimal investment and risk control for competitive insurers," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 202-217.
    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. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," Papers 2304.07108, arXiv.org, revised Oct 2023.
    8. Masaaki Fujii & Masashi Sekine, 2024. "Mean field equilibrium asset pricing model with habit formation," Papers 2406.02155, arXiv.org, revised Nov 2024.

    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. Guanxing Fu & Chao Zhou, 2023. "Mean field portfolio games," Finance and Stochastics, Springer, vol. 27(1), pages 189-231, January.
    2. Guanxing Fu & Xizhi Su & Chao Zhou, 2020. "Mean Field Exponential Utility Game: A Probabilistic Approach," Papers 2006.07684, arXiv.org, revised Jul 2020.
    3. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.
    4. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," Papers 2304.07108, arXiv.org, revised Oct 2023.
    5. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field equilibrium price formation with exponential utility," CARF F-Series CARF-F-559, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    7. Ludovic Tangpi & Xuchen Zhou, 2022. "Optimal Investment in a Large Population of Competitive and Heterogeneous Agents," Papers 2202.11314, arXiv.org, revised Feb 2023.
    8. 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.
    9. Ruimeng Hu & Thaleia Zariphopoulou, 2021. "$N$-player and Mean-field Games in It\^{o}-diffusion Markets with Competitive or Homophilous Interaction," Papers 2106.00581, arXiv.org, revised Jun 2021.
    10. Lijun Bo & Shihua Wang & Xiang Yu, 2021. "Mean Field Game of Optimal Relative Investment with Jump Risk," Papers 2108.00799, arXiv.org, revised Feb 2023.
    11. Guanxing Fu, 2023. "Mean field portfolio games with consumption," Mathematics and Financial Economics, Springer, volume 17, number 4, December.
    12. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    13. Wahid Faidi, 2022. "Optimal investment and consumption under logarithmic utility and uncertainty model," Papers 2211.05367, arXiv.org, revised Jun 2024.
    14. 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.
    15. Mastrolia, Thibaut, 2018. "Density analysis of non-Markovian BSDEs and applications to biology and finance," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 897-938.
    16. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    17. M. Nabil Kazi-Tani & Dylan Possamai & Chao Zhou, 2014. "Quadratic BSDEs with jumps: related non-linear expectations," Papers 1403.2730, arXiv.org.
    18. Lionnet, Arnaud, 2014. "Some results on general quadratic reflected BSDEs driven by a continuous martingale," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1275-1302.
    19. Masaaki Fujii & Masashi Sekine, 2024. "Mean field equilibrium asset pricing model with habit formation," Papers 2406.02155, arXiv.org, revised Nov 2024.
    20. Zongxia Liang & Keyu Zhang, 2023. "Time-inconsistent mean field and n-agent games under relative performance criteria," Papers 2312.14437, arXiv.org, revised Apr 2024.

    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:2106.06185. 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.