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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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Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...
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) | ||||
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Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics |
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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: |
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Number: | No.806 | ||||
Number of Pages: | 8 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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