IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1911.09441.html
   My bibliography  Save this paper

Some analytically solvable problems of the mean-field games theory

Author

Listed:
  • Sergey I. Nikulin
  • Olga S. Rozanova

Abstract

We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice of data, this problem can be reduced to solving a quadratically nonlinear system of ODEs. This situation occurs naturally in economic applications. As an example, the problem of forming an investor's opinion on an asset is considered.

Suggested Citation

  • Sergey I. Nikulin & Olga S. Rozanova, 2019. "Some analytically solvable problems of the mean-field games theory," Papers 1911.09441, arXiv.org.
    • Handle: RePEc:arx:papers:1911.09441
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1911.09441
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bielecki, Tomasz R. & Pliska, Stanley R. & Sherris, Michael, 2000. "Risk sensitive asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1145-1177, 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. Leitner Johannes, 2005. "Optimal portfolios with expected loss constraints and shortfall risk optimal martingale measures," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 49-66, January.
    2. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    3. Lijuan Xu & Abbas Ali Chandio & Jingyi Wang & Yuansheng Jiang, 2022. "Does Farmland Tenancy Improve Household Asset Allocation? Evidence from Rural China," Land, MDPI, vol. 12(1), pages 1-22, December.
    4. O. S. Rozanova & G. S. Kambarbaeva, 2015. "Optimal strategies of investment in a linear stochastic model of market," Papers 1501.07124, arXiv.org.
    5. Guidolin, Massimo & Timmermann, Allan, 2007. "Asset allocation under multivariate regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3503-3544, November.
    6. Vladislav Kargin, 2003. "Optimal Convergence Trading," Papers math/0302104, arXiv.org, revised Aug 2003.
    7. Hanchao Liu & Dena Firoozi, 2024. "Hilbert Space-Valued LQG Mean Field Games: An Infinite-Dimensional Analysis," Papers 2403.01012, arXiv.org.
    8. Tadashi Hayashi & Jun Sekine, 2011. "Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 385-403, November.
    9. Toshiki Honda & Shoji Kamimura, 2011. "On the Verification Theorem of Dynamic Portfolio-Consumption Problems with Stochastic Market Price of Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(2), pages 151-166, May.
    10. Aivaliotis, Georgios & Palczewski, Jan, 2014. "Investment strategies and compensation of a mean–variance optimizing fund manager," European Journal of Operational Research, Elsevier, vol. 234(2), pages 561-570.
    11. Michael Stutzer, 2011. "Portfolio choice with endogenous utility: a large deviations approach," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 43, pages 619-640, World Scientific Publishing Co. Pte. Ltd..
    12. Hanchao Liu & Dena Firoozi & Mich`ele Breton, 2023. "LQG Risk-Sensitive Single-Agent and Major-Minor Mean Field Game Systems: A Variational Framework," Papers 2305.15364, arXiv.org, revised Aug 2023.

    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:1911.09441. 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.