IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i8p2401-2435.html
   My bibliography  Save this article

Limit theorems for individual-based models in economics and finance

Author

Listed:
  • Remenik, Daniel

Abstract

There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions between agents. Our purpose is to present a general framework that encompasses a broad range of models, by proving a law of large numbers and a central limit theorem for certain interacting particle systems with very general state spaces. To do this we draw inspiration from some work done in mathematical ecology and mathematical physics. The first result is proved for the system seen as a measure-valued process, while to prove the second one we will need to introduce a chain of embeddings of some abstract Banach and Hilbert spaces of test functions and prove that the fluctuations converge to the solution of a certain generalized Gaussian stochastic differential equation taking values in the dual of one of these spaces.

Suggested Citation

  • Remenik, Daniel, 2009. "Limit theorems for individual-based models in economics and finance," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2401-2435, August.
  • Handle: RePEc:eee:spapps:v:119:y:2009:i:8:p:2401-2435
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00187-7
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Steffen Huck & Michael Kosfeld, 2007. "The Dynamics of Neighbourhood Watch and Norm Enforcement," Economic Journal, Royal Economic Society, vol. 117(516), pages 270-286, January.
    2. Darrell Duffie, 2012. "Over-The-Counter Markets," Introductory Chapters,in: Dark Markets: Asset Pricing and Information Transmission in Over-the-Counter Markets Princeton University Press.
    3. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
    4. Darrell Duffie & Gustavo Manso, 2007. "Information Percolation in Large Markets," American Economic Review, American Economic Association, vol. 97(2), pages 203-209, May.
    5. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    Full references (including those not matched with items on IDEAS)

    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:119:y:2009:i:8:p:2401-2435. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.