The exact law of large numbers via Fubini extension and characterization of insurable risks

• 成果类型: Article
• 署名作者: Sun, YN
• 署名单位: National University of Singapore; National University of Singapore
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2004.10.005
• 发表日期: 2006
• 页码: 31-69
• 关键词: exact law of large numbers; Fubini extension; uncorrelatedness and independence; insurable risks; rich product probability space; Pareto optimality and equilibrium

摘要

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. (c) 2005 Elsevier Inc. All rights reserved.