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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.

Suggested Citation

  • Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    • Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:432-443
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    References listed on IDEAS

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    More about this item

    Keywords

    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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