On the Equivalence of Conglomerability and Disintegrability for Unbounded Random Variables.∗ by Mark J. Schervish, Teddy Seidenfeld
نویسنده
چکیده
We extend a result of Dubins (1975) from bounded to unbounded random variables. Dubins (1975) showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglomerability). We give a sufficient condition to extend this result to the collection of all random variables that have finite expected value and whose conditional expectations are finite and have finite expected value.
منابع مشابه
On the equivalence of conglomerability and disintegrability for unbounded random variables
We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectat...
متن کاملInfinite Previsions and Finitely Additive Expectations
We give an extension of de Finetti’s concept of coherence to unbounded (but real-valued) random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of th...
متن کاملWhen coherent preferences may not preserve indifference between equivalent random variables: A price for unbounded utilities
We extend de Finetti’s (1974) theory of coherence to apply also to unbounded random variables. We show that for random variables with mandated infinite prevision, such as for the St. Petersburg gamble, coherence precludes indifference between equivalent random quantities. That is, we demonstrate when the prevision of the difference between two such equivalent random variables must be positive. ...
متن کاملThe fundamental theorems of prevision and asset pricing
We explore two connections between the concepts of coherence, as defined by de Finetti, and arbitrage-free asset pricing in financial markets. We contrast these concepts when random quantities may be unbounded. And we discuss some of the consequences for arbitrage theory when coherent previsions are merely finitely (but not countably) additive. 2007 Elsevier Inc. All rights reserved.
متن کاملDominating countably many forecasts
We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts. 1. Introducti...
متن کامل