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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

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    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp_806.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    3. 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.
    4. M. Ali Khan & Yeneng Sun, 1999. "Weak measurability and characterizations of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 541-560.
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