THE DECOMPOSITION OF RISK IN DENUMERABLE POPULATIONS WITH EX ANTE IDENTICAL INDIVIDUALS
Abstract This paper proposes a framework for the decomposition of risk into an aggregate and an idiosyncratic component which sidesteps the difficulties inherent in continuums of random variables, addressed recently in Al Najjar (Econometrica63(1995), 1195–1224). It assumes that the population is denumerable and that individuals are indistinguishableex ante. In that context, a factorization of risk exists. Aσ-field of aggregate events can be identified, which is such that all aggregate quantities are measurable with respect to it. Furthermore, the individual characteristics are independent and identically distributed across agents conditionally on the aggregateσ-field.Journal of Economic LiteratureClassification Numbers: Z00, G19.