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Individual Risk and Lebesgue Extension without Aggregate Uncertainty

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Author Info
Sun, Yeneng
Zhang , Yongchao

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Abstract

Many economic models include random shocks imposed on a large number (continuum) of economic agents with individual risk. In this context, an exact law of large numbers and its converse is presented in Sun (2006) to characterize the cancelation of individual risk via aggregation. However, it is well known that the Lebesgue unit interval is not suitable for modeling a continuum of agents in the particular setting. The purpose of this note is to show that an extension of the Lebesgue unit interval does work well as an agent space with various desirable properties associated with individual risk.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7448.

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Date of creation: 29 Feb 2008
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Handle: RePEc:pra:mprapa:7448

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Related research
Keywords: No aggregate uncertainty independence exact law of large numbers Fubini extension Lebesgue measure.

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Find related papers by JEL classification:
C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
E00 - Macroeconomics and Monetary Economics - - General - - - General
D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General

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  1. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2004. "Over-the-Counter Markets," NBER Working Papers 10816, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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    • Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2005. "Over-the-Counter Markets," Econometrica, Econometric Society, vol. 73(6), pages 1815-1847, November. [Downloadable!] (restricted)
  2. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Core, equilibria and incentives in large asymmetric information economies," Games and Economic Behavior, Elsevier, vol. 61(1), pages 131-155, October. [Downloadable!] (restricted)
  3. McLean, Richard & Postlewaite, Andrew, 2005. "Core convergence with asymmetric information," Games and Economic Behavior, Elsevier, vol. 50(1), pages 58-78, January. [Downloadable!] (restricted)
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  4. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February. [Downloadable!] (restricted)
  5. Ricardo Lagos & Guillaume Rocheteau, 2007. "Liquidity in asset markets with search frictions," Working Paper 0706, Federal Reserve Bank of Cleveland. [Downloadable!]
  6. Pierre-Olivier Weill, 2007. "Leaning Against the Wind," Review of Economic Studies, Blackwell Publishing, vol. 74(4), pages 1329-1354, October. [Downloadable!] (restricted)
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  7. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November. [Downloadable!] (restricted)
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  8. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January. [Downloadable!] (restricted)
  9. Peter J. Hammond & Yeneng Sun, 2000. "Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables," Working Papers 00008, Stanford University, Department of Economics. [Downloadable!]
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