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Differentiability properties of Rank-Linear Utilities

Carlier, Guillaume (2008), Differentiability properties of Rank-Linear Utilities, Journal of Mathematical Economics, 44, 1, p. 15-23. http://dx.doi.org/10.1016/j.jmateco.2007.04.002

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Type
Article accepté pour publication ou publié
Date
2008
Journal name
Journal of Mathematical Economics
Volume
44
Number
1
Publisher
Elsevier
Pages
15-23
Publication identifier
Metadata
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Author(s)
Carlier, Guillaume
Abstract (EN)
We study the differentiability properties of concave functionals defined as integrals of the quantile. These functionals generalize the rank dependent expected utility and are called rank-linear utilities in decision theory. Their superdifferential is described as well as the set of random variables where they are Gâteaux-differentiable. Our results generalize those obtained for the rank dependent expected utility in Ref. [Carlier, G., Dana, R.-A., 2003. Core of a convex distortion of a probability. Journal of Economic Theory 113, 199–222.].
Subjects / Keywords
Optimization and control
JEL
C44 - Operations Research; Statistical Decision Theory