Simple axioms for countably additive subjective probability
AbstractThis 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 5 (September)
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Web page: http://www.elsevier.com/locate/jmateco
Subjective probability Monotone Continuity Countable additivity Exponential time discounting;
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- Harvey, Charles M. & Østerdal, Lars Peter, 2012. "Discounting models for outcomes over continuous time," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 284-294.
- Spinu, Vitalie & Wakker, Peter P., 2013. "Expected utility without continuity: A comment on Delbaen et al. (2011)," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 28-30.
- Kopylov, Igor, 2010. "Unbounded probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 113-118, September.
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