Hammond, Peter J. and Sun, Yeneng (2007) Characterization of risk: a sharp law of large numbers. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.806).

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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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Hilbert space, Stochastic partial differential equations, Risk -- Mathematical models, Law of large numbers, Mathematical statistics
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Official Date:	2007
Dates:	Date Event 2007 Published
Number:	No.806
Number of Pages:	8
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access

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