The exact law of large numbers via Fubini extension and characterization of insurable risks [An article from: Journal of Economic Theory]

by Y.N. Sun

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This digital document is a journal article from Journal of Economic Theory, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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A Fubini extension is formally introduced as a probability space that extends the usual product probability space and retains the Fubini property. Simple measure-theoretic methods are applied to this framework to obtain various versions of the exact law of large numbers and their converses for a continuum of random variables or stochastic processes. A model for a large economy with individual risks is developed; and insurable risks are characterized by essential pairwise independence. The usual continuum product based on the Kolmogorov construction together with the Lebesgue measure as well as the usual finitely additive measure-theoretic framework is shown further to be not suitable for modeling individual risks. Measurable processes with essentially pairwise independent random variables that have any given variety of distributions exist in a rich product probability space that can also be constructed by extending the usual continuum product.

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