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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 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.

Suggested Citation

  • Sun, Yeneng & Zhang, Yongchao, 2008. "Individual Risk and Lebesgue Extension without Aggregate Uncertainty," MPRA Paper 7448, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7448

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    References listed on IDEAS

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    5. Yeneng Sun & Nicholas Yannelis, 2008. "Ex ante efficiency implies incentive compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 35-55, July.
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    7. Pierre-Olivier Weill, 2007. "Leaning Against the Wind," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1329-1354.
    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. 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.
    10. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
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    Cited by:

    1. Yu, Haomiao & Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 2015. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society, vol. 10(1), January.
    2. Duffie, Darrell & Sun, Yeneng, 2012. "The exact law of large numbers for independent random matching," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1105-1139.
    3. repec:eee:jetheo:v:174:y:2018:i:c:p:124-183 is not listed on IDEAS
    4. Martin Hellwig, 2010. "Utilitarian mechanism design for an excludable public good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 361-397, September.
    5. Mendolicchio, Concetta & Paolini, Dimitri & Pietra, Tito, 2012. "Investments in education and welfare in a two-sector, random matching economy," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 367-385.
    6. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    7. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    8. Marcel Nutz, 2016. "A Mean Field Game of Optimal Stopping," Papers 1605.09112,, revised Nov 2017.
    9. Duffie, Darrell & Qiao, Lei & Sun, Yeneng, 2015. "Dynamic Directed Random Matching," Research Papers 3359, Stanford University, Graduate School of Business.
    10. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
    11. Martin Hellwig, 2011. "Incomplete-Information Models of Large Economies with Anonymity: Existence and Uniqueness of Common Priors," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2011_08, Max Planck Institute for Research on Collective Goods.
    12. Lei Qiao & Yeneng Sun & Zhixiang Zhang, 2016. "Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 43-64, June.
    13. Patrizia Berti & Michele Gori & Pietro Rigo, 2009. "A note on the law of large numbers in economics," Working Papers - Mathematical Economics 2009-10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Nov 2010.
    14. Xiang Sun & Yongchao Zhang, 2015. "Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 161-182, January.
    15. Yeneng Sun & Lei Wu & Nicholas C. Yannelis, 2011. "Existence, Incentive Compatibility and Efficiency of the Rational Expectations Equilibrium," The School of Economics Discussion Paper Series 1108, Economics, The University of Manchester.
    16. 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.
    17. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308,
    18. repec:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0010-8 is not listed on IDEAS

    More about this item


    No aggregate uncertainty; independence; exact law of large numbers; Fubini extension; Lebesgue measure;

    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; Programming Models; Mathematical and Simulation Modeling - - - General

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