Characterization of Risk: A Sharp Law of Large Numbers

Peter Hammond and Yeneng Sun ()

The Warwick Economics Research Paper Series (TWERPS) from University of Warwick, Department of Economics

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.

Pages: 8 pages
Date: 2007
New Economics Papers: this item is included in nep-sea
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Persistent link: https://EconPapers.repec.org/RePEc:wrk:warwec:806

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