Characterization of Risk : A Sharp Law of Large Numbers
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  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.
|Date of creation:||2007|
|Contact details of provider:|| Postal: CV4 7AL COVENTRY|
Phone: +44 (0) 2476 523202
Fax: +44 (0) 2476 523032
Web page: http://www2.warwick.ac.uk/fac/soc/economics/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
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)
If references are entirely missing, you can add them using this form.