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Individual risk and Lebesgue extension without aggregate uncertainty

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  • Sun, Yeneng
  • Zhang, Yongchao

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 [Y.N. Sun, The exact law of large numbers via Fubini extension and characterization of insurable risks, J. Econ. Theory 126 (2006) 31-69] to characterize the cancellation 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 paper 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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 1 (January)
Pages: 432-443

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:432-443

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: No aggregate uncertainty Independence Exact law of large numbers Fubini extension Lebesgue measure;

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References

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  1. Yeneng Sun & Nicholas Yannelis, 2008. "Ex ante efficiency implies incentive compatibility," Economic Theory, Springer, vol. 36(1), pages 35-55, July.
  2. Ricardo Lagos & Guillaume Rocheteau, 2008. "Liquidity in asset markets with search frictions," Staff Report 408, Federal Reserve Bank of Minneapolis.
  3. Pierre-Olivier Weill, 2007. "Leaning Against the Wind," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1329-1354.
  4. Anderson, Robert M., 1991. "Non-standard analysis with applications to economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 39, pages 2145-2208 Elsevier.
  5. 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.
  6. 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.
  7. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
  8. Richard McLean & Andrew Postlewaite, . "Informational Size and Incentive Compatibility," CARESS Working Papres 99-14, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  9. Duffie, Darrell & Garleanu, Nicolae Bogdan & Pedersen, Lasse Heje, 2006. "Valuation in Over-the-Counter Markets," CEPR Discussion Papers 5491, C.E.P.R. Discussion Papers.
  10. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2004. "Over-the-Counter Markets," NBER Working Papers 10816, National Bureau of Economic Research, Inc.
  11. 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.
  12. 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.
  13. Richard McLean & Andrew Postlewaite, 2003. "Core Convergence with Asymmetric Information," PIER Working Paper Archive 03-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  14. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
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Citations

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Cited by:
  1. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2012. "Large Games with a Bio-Social Typology," Working Papers 035, Ryerson University, Department of Economics.
  2. Darrell Duffie & Yeneng Sun, 2004. "The Exact Law of Large Numbers for Independent Random Matching," Levine's Bibliography 122247000000000328, UCLA Department of Economics.
  3. C. Mendolicchio & D. Paolini & T. Pietra, 2010. "Investments in education and welfare in a two-sector, random matching economy," Working Papers 702, Dipartimento Scienze Economiche, Universita' di Bologna.
  4. Martin Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer, vol. 44(3), pages 361-397, September.
  5. Patrizia Berti & Michele Gori & Pietro Rigo, 2010. "A note on the law of large numbers in economics," Quaderni di Dipartimento 131, University of Pavia, Department of Economics and Quantitative Methods.
  6. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer, vol. 55(2), pages 457-479, February.
  7. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer, vol. 45(1), pages 1-22, October.
  8. Yu, Haomiao & Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 0. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society.
  9. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Working Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
  10. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.

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