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Individual risk and Lebesgue extension without aggregate uncertainty

  • Sun, Yeneng
  • Zhang, Yongchao

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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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, 2007. "Liquidity in asset markets with search frictions," Working Paper 0706, Federal Reserve Bank of Cleveland.
  3. 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.
  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. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2006. "Valuation in Over-the-Counter Markets," NBER Working Papers 12020, National Bureau of Economic Research, Inc.
  6. Pierre-Olivier Weill, 2007. "Leaning Against the Wind," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1329-1354.
  7. 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.
  8. 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.
  9. Darrell Duffie & Nicolae Garleanu & Lasse Heje Pedersen, 2005. "Over-the-Counter Markets," Econometrica, Econometric Society, vol. 73(6), pages 1815-1847, November.
  10. McLean, Richard & Postlewaite, Andrew, 2005. "Core convergence with asymmetric information," Games and Economic Behavior, Elsevier, vol. 50(1), pages 58-78, January.
  11. 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.
  12. 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.
  13. 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.
  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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