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Characterization of Risk : A Sharp Law of Large Numbers

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Author Info
Hammond, Peter J. (Department of Economics, University of Warwick,)
Sun, Yeneng (Department of Economics, National University of Singapore)

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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.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/publications/twerp_806.pdf
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Publisher Info
Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 806.

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Length: 8 pages
Date of creation: 2007
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Handle: RePEc:wrk:warwec:806

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  1. 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. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
  3. 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.
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This page was last updated on 2009-11-30.

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