Decomposition-integral: unifying Choquet and the concave integrals View Full Text


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Article Info

DATE

2013-11-02

AUTHORS

Yaarit Even, Ehud Lehrer

ABSTRACT

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A prespecified set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is defined as the highest of these values. Thus, different sets of collections induce different decomposition-integrals. It turns out that this decomposition approach unifies well-known integrals, such as Choquet, the concave and Riemann integral. Decomposition-integrals are investigated with respect to a few essential properties that emerge in economic contexts, such as concavity (uncertainty-aversion), monotonicity with respect to stochastic dominance and translation-covariance. The paper characterizes the sets of collections that induce decomposition-integrals, which respect each of these properties. More... »

PAGES

33-58

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00199-013-0780-0

DOI

http://dx.doi.org/10.1007/s00199-013-0780-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005818471


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