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Simple axioms for countably additive subjective probability

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  • Kopylov, Igor

Abstract

This paper refines Savage's theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow's (1970) Monotone Continuity. Second, I relax Savage's primitives: in my framework, the class of events need not be a [sigma]-algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory's unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set.

Suggested Citation

  • Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:5:p:867-876
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    References listed on IDEAS

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    1. Peter Wakker, 1993. "Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 487-493.
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