Characterization of risk: a sharp law of large numbers
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...
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  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|
|Number of Pages:||8|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
 C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 2nd edition, Springer, New York, 1999.
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