Time Continuity and Nonadditive Expected Utility

Information consisting of probabilities of some (but possibly not all) events induces an integral with respect to a probability specified on a subalgebra. A decision maker evaluates the alternatives using only the available information and completely ignoring unavailable information. Assume now that...

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Veröffentlicht in:	Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 34(2009), 3, Seite 661-673
1. Verfasser:	Teper, Roee (VerfasserIn)
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2009
Zugriff auf das übergeordnete Werk:	Mathematics of Operations Research
Schlagworte:	time continuity partially specified probabilities induced capacity Choquet integral Primary 91B06 Primary 62C99 Primary 91B08 secondary 60F99 Primary: decision analysis/theory secondary: probability mehr... Mathematics Economics Applied sciences


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520			\|a Information consisting of probabilities of some (but possibly not all) events induces an integral with respect to a probability specified on a subalgebra. A decision maker evaluates the alternatives using only the available information and completely ignoring unavailable information. Assume now that the decision maker assesses the worth of a different lottery at each point in a discrete time. Assume also that each such lottery is preferred to some fixed alternative lottery. Now, consider the situation where the sequence of lotteries converges in some sense. If the limiting lottery is preferred to the fixed alternative, then the preference order is referred to as time continuous. This paper studies time continuity for two preference functionals: the Choquet integral and the integral with respect to a probability specified on a subalgebra. The integral with respect to probability specified on a subalgebra is determined by the structure of the available information. By relating it to the Choquet integral, we characterize the structure of available information that would yield time continuity.
540			\|a Copyright 2009 Institute for Operations Research and the Management Sciences
650		4	\|a time continuity
650		4	\|a partially specified probabilities
650		4	\|a induced capacity
650		4	\|a Choquet integral
650		4	\|a Primary 91B06
650		4	\|a Primary 62C99
650		4	\|a Primary 91B08
650		4	\|a secondary 60F99
650		4	\|a Primary: decision analysis/theory
650		4	\|a secondary: probability
650		4	\|a Mathematics \|x Mathematical objects \|x Mathematical sequences \|x Increasing sequences
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical theorems
650		4	\|a Mathematics \|x Mathematical analysis \|x Mathematical continuity
650		4	\|a Economics \|x Microeconomics \|x Economic utility \|x Expected utility
650		4	\|a Mathematics \|x Pure mathematics \|x Calculus \|x Differential calculus \|x Mathematical integration \|x Mathematical integrals
650		4	\|a Applied sciences \|x Computer science \|x Artificial intelligence \|x Machine learning \|x Perceptron convergence procedure
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Probabilities
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Measures of variability \|x Multivariate statistical analysis \|x Covariance
650		4	\|a Mathematics \|x Mathematical objects \|x Mathematical sequences \|x Increasing sequences
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical theorems
650		4	\|a Mathematics \|x Mathematical analysis \|x Mathematical continuity
650		4	\|a Economics \|x Microeconomics \|x Economic utility \|x Expected utility
650		4	\|a Mathematics \|x Pure mathematics \|x Calculus \|x Differential calculus \|x Mathematical integration \|x Mathematical integrals
650		4	\|a Applied sciences \|x Computer science \|x Artificial intelligence \|x Machine learning \|x Perceptron convergence procedure
650		4	\|a Mathematics \|x Mathematical expressions \|x Mathematical functions
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Probabilities
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Descriptive statistics \|x Measures of variability \|x Multivariate statistical analysis \|x Covariance
655		4	\|a research-article
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