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Do law-invariant linear functionals collapse to the mean?.
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In this paper, it was shown that a law-invariant bounded linear functional is a scalar multiple of the expectation in a rearrangement invariant space, and that this property fails on a wide range of rearrangements.Abstract:
In this note, we show that, on a wide range of rearrangement-invariant spaces, a law-invariant bounded linear functional is a scalar multiple of the expectation. We also construct a rearrangement-invariant space on which this property fails.read more
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A Framework for Measures of Risk under Uncertainty
TL;DR: In this article, a unified axiomatic framework for risk evaluation principles is proposed, which quantifies jointly a loss random variable and a set of plausible probabilities, called generalized risk measure.
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Book
Classical Banach spaces
Joram Lindenstrauss,L. Tzafriri +1 more
TL;DR: Springer-Verlag is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers.
Book
Interpolation of operators
C. Bennett,M Sharpley +1 more
TL;DR: In this article, the classical interpolation theorem is extended to the Banach Function Spaces, and the K-Method is used to find a Banach function space with a constant number of operators.
Book ChapterDOI
On law invariant coherent risk measures
TL;DR: In this paper, a special class of coherent risk measures is defined and a characterization of it is given, where the probability space is defined as a probability space and the coherent risk measure is defined in terms of a probability vector.
Journal ArticleDOI
Distribution-invariant risk measures, information, and dynamic consistency
TL;DR: In this article, the authors characterize distribution-invariant risk measures with convex acceptance and rejection sets on the level of distributions and show that these risk measures are closely related to utility-based shortfall risk.
Book ChapterDOI
Law invariant risk measures have the Fatou property
TL;DR: In this paper, a dual characterization of law invariant coherent risk measures, satisfying the Fatou property, was given, and it was shown that the hypothesis of Fatou properties may actually be dropped as it is automatically implied by the hypothesis for law invariance.