Decomposition-integral: unifying Choquet and the concave integrals

Yaarit Even and Ehud Lehrer ()

Economic Theory, 2014, vol. 56, issue 1, 33-58

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Capacity; Non-additive probability; Decision making; Decomposition-integral; Concave integral; Choquet integral; C71; D80; D81; D84 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (17)

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DOI: 10.1007/s00199-013-0780-0

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