IDEAS home Printed from https://ideas.repec.org/p/wrk/warwec/806.html
   My bibliography  Save this paper

Characterization of Risk : A Sharp Law of Large Numbers

Author

Listed:
  • Hammond, Peter J.

    (Department of Economics, University of Warwick,)

  • Sun, Yeneng

    (Department of Economics, National University of Singapore)

Abstract

An extensive literature in economics uses a continuum of random variables to model individual random shocks imposed on a large population. Let H denote the Hilbert space of square-integrable random variables. A key concern is to characterize the family of all H-valued functions that satisfy the law of large numbers when a large sample of agents is drawn at random. We use the iterative extension of an infinite product measure introduced in [6] to formulate a “sharp” law of large numbers. We prove that an H-valued function satisfies this law if and only if it is both Pettis-integrable and norm integrably bounded.

Suggested Citation

  • Hammond, Peter J. & Sun, Yeneng, 2007. "Characterization of Risk : A Sharp Law of Large Numbers," The Warwick Economics Research Paper Series (TWERPS) 806, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:806
    as

    Download full text from publisher

    File URL: https://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp_806.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Al-Najjar, Nabil Ibraheem, 1995. "Decomposition and Characterization of Risk with a Continuum of Random Variables," Econometrica, Econometric Society, vol. 63(5), pages 1195-1224, September.
    2. Nabil I. Al-Najjar, 1999. "Decomposition and Characterization of Risk with a Continuum of Random Variables: Corrigendum," Econometrica, Econometric Society, vol. 67(4), pages 919-920, July.
    3. Hammond, Peter J. & Sun, Yeneng, 2007. "Monte Carlo Simulation of Macroeconomic Risk with a Continuum Agents : The General Case," The Warwick Economics Research Paper Series (TWERPS) 803, University of Warwick, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    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:wrk:warwec:806. 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: (Margaret Nash). General contact details of provider: http://edirc.repec.org/data/dewaruk.html .

    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.