Book ChapterDOI
Law invariant convex risk measures
Marco Frittelli,Emanuela Rosazza Gianin +1 more
- Vol. 7, pp 33-46
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In this paper, the representation of law invariant convex risk measures is provided, as a generalization of a result by Kusuoka (2001), and very particular cases of law-invariant coherent risk measures are studied.Abstract:
As a generalization of a result by Kusuoka (2001), we provide the representation of law invariant convex risk measures. Very particular cases of law invariant coherent and convex risk measures are also studied.read more
Citations
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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
Law Invariant Risk Measures Have the Fatou Property
TL;DR: In this article, a dual characterization of law invariant coherent risk measures, satisfying the Fatou property, was given, and the notion of the Lebesgue property of a convex risk measure was introduced.
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
Risk measures on orlicz hearts
Patrick Cheridito,Tianhui Li +1 more
TL;DR: In this paper, it was shown that every coherent or convex monetary risk measure on an Orlicz heart which is real-valued on a set with non-empty algebraic interior admits a robust representation as maximal penalized expectation with respect to different probability measures.
Journal ArticleDOI
Modeling and optimization of risk
TL;DR: The most recent advances in the context of decision making under uncertainty are surveyed, with an emphasis on the modeling of risk-averse preferences using the apparatus of axiomatically defined risk functionals and their connection to utility theory, stochastic dominance, and other more established methods.
References
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Journal ArticleDOI
Coherent Measures of Risk
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Book
Probability with martingales
TL;DR: A branching-process example and an easy strong law: product measure using martingale theory and the central limit theorem are presented.
Book
Stochastic Finance: An Introduction in Discrete Time
Hans Föllmer,Alexander Schied +1 more
TL;DR: In this article, the authors present an introduction to financial mathematics, focusing on stochastic models in discrete time, with a focus on the problem of pricing and hedging of financial derivatives.
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.
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Convex measures of risk and trading constraints
Hans Föllmer,Alexander Schied +1 more
TL;DR: The notion of a convex measure of risk is introduced, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and a corresponding extensions of the representation theorem in terms of probability measures on the underlying space of scenarios are proved.