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Characterization of risk: a sharp law of large numbers
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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 squareintegrable random variables. A key concern is to characterize the family of all Hvalued 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 Hvalued function satisfies this law if and only if it is both Pettisintegrable 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 
Number:  No.806 
Number of Pages:  8 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
References:  [1] C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 2nd edition, Springer, New York, 1999. 
URI:  http://wrap.warwick.ac.uk/id/eprint/1407 
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