Law-Invariant Functionals on General Spaces of Random Variables
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In this article, general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals are established.Abstract:
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literature to a large clas...read more
Citations
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Journal ArticleDOI
Law-invariant functionals that collapse to the mean
TL;DR: In this paper, it was shown that the expectation functional is the only law-invariant convex functional that is linear along the direction of a nonconstant random variable with nonzero expectation.
Journal ArticleDOI
Adjusted Expected Shortfall
TL;DR: In this article , the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution are studied.
Journal ArticleDOI
Adjusted Expected Shortfall
TL;DR: In this article, the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution are studied.
Posted Content
Law-invariant functionals that collapse to the mean: Beyond convexity
TL;DR: In this paper, the authors established general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation, and provided a complete account of the collapse-to-mean for quasiconvex functionals.
Journal ArticleDOI
Automatic Fatou property of law-invariant risk measures
TL;DR: In this article , the authors investigated automatic Fatou property of law-invariant risk measures on a rearrangement-inherent function space X other than L∞ and showed that under the AOCEA property, every real-valued, law invariant, coherent risk measure on X admits a tractable dual representation at every variable X ∈ X whose negative tails have vanishing norm.
References
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Journal ArticleDOI
Convex measures of risk and trading constraints
Hans Föllmer,Alexander Schied +1 more
TL;DR: In this paper, the authors introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and prove a corresponding extension of representation theorem in terms of probability measures on the underlying space of scenarios.
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.
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.
Journal ArticleDOI
Optimal risk sharing for law invariant monetary utility functions
TL;DR: In this paper, the authors consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law invariant risk measures.
Journal ArticleDOI
Comparative and qualitative robustness for law-invariant risk measures
TL;DR: In this paper, the authors argue that Hampel's classical notion of qualitative robustness is not suitable for risk measurement, and propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz spaces.
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