This paper develops a framework in which a model with a continuum of agents and with individual and aggregate risks can be viewed as an idealization of large finite economies. The paper identifies conditions under which a sequence of finite economies gives rise to a limiting continuum economy in which uncertainty has a simple structure. The state space is the product of aggregate states and micro-states; aggregate states represent economy-wide random aggregate fluctuations, while micro-states reflect individual shocks which fluctuate independently around aggregate states and have no further discernible structure. In the special case where shocks in the finite economies are exchangable, the limiting economy satisfies a continuum-version of de Finetti's Theorem. The paper then uses this framework to derive implications for the interpretations of the Strong Law of Large Numbers and the Pettis Integral.
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number
1160.
Length: Date of creation: Mar 1996 Date of revision: Handle: RePEc:nwu:cmsems:1160
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Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997.
"Patterns, Types, and Bayesian Learning,"
Discussion Papers
1177, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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