scholarly journals Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces

2018 ◽  
Vol 22 (2) ◽  
pp. 395-415 ◽  
Author(s):  
Niushan Gao ◽  
Denny Leung ◽  
Cosimo Munari ◽  
Foivos Xanthos
Keyword(s):  
Risk Measures ◽  
Orlicz Spaces ◽  
Fatou Property ◽  
Law Invariant Risk Measures

scholarly journals Law invariant risk measures have the Fatou property

2007 ◽  
pp. 49-71 ◽  
Author(s):  
Elyès Jouini ◽  
Walter Schachermayer ◽  
Nizar Touzi
Keyword(s):  
Risk Measures ◽  
Fatou Property ◽  
Law Invariant Risk Measures

scholarly journals Law Invariant Risk Measures Have the Fatou Property

2005 ◽  
Author(s):  
Elyes Jouini ◽  
Walter Schachermayer ◽  
Nizar Touzi
Keyword(s):  
Risk Measures ◽  
Fatou Property ◽  
Law Invariant Risk Measures

Lebesgue property for convex risk measures on Orlicz spaces

2012 ◽  
Vol 6 (1) ◽  
pp. 15-35 ◽  
Author(s):  
J. Orihuela ◽  
M. Ruiz Galán
Keyword(s):  
Risk Measures ◽  
Orlicz Spaces ◽  
Convex Risk Measures

scholarly journals Law invariant risk measures and information divergences

2018 ◽  
Vol 6 (1) ◽  
pp. 228-258
Author(s):  
Daniel Lacker
Keyword(s):  
Relative Entropy ◽  
Risk Measures ◽  
Time Consistency ◽  
Probability Measures ◽  
Classical Information ◽  
Natural Properties ◽  
Certainty Equivalents ◽  
Shortfall Risk ◽  
Information Divergence ◽  
Law Invariant Risk Measures

AbstractAone-to-one correspondence is drawnbetween lawinvariant risk measures and divergences,which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy and convex f -divergences. Several properties of divergence and their duality with law invariant risk measures are characterized, such as joint semicontinuity and convexity, and we notably relate their chain rules or additivity properties with certain notions of time consistency for dynamic law risk measures known as acceptance and rejection consistency. The examples of shortfall risk measures and optimized certainty equivalents are discussed in detail.

BALAYAGE MONOTONOUS RISK MEASURES

2004 ◽  
Vol 07 (07) ◽  
pp. 887-900 ◽  
Author(s):  
JOHANNES LEITNER
Keyword(s):  
Risk Measures ◽  
Equivalent Condition ◽  
Coherent Risk Measures ◽  
Fatou Property ◽  
Coherent Risk ◽  
Representation Result

We consider coherent risk measures satisfying the Fatou property which are monotonous with respect to balayage or dilatation. An equivalent condition ensuring balayage-monotonicity is given and a representation result is derived.

scholarly journals Surplus-Invariant Risk Measures

2020 ◽  
Vol 45 (4) ◽  
pp. 1342-1370 ◽  
Author(s):  
Niushan Gao ◽  
Cosimo Munari
Keyword(s):  
Systematic Study ◽  
Risk Measures ◽  
Orlicz Spaces ◽  
Capital Requirements ◽  
Vector Lattices ◽  
Dual Representations ◽  
Robust Model ◽  
Model Spaces ◽  
Acceptance Sets ◽  
Lattice Approach

This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper, we develop a theory of surplus invariance in its natural framework, namely, that of vector lattices. Besides providing a unifying perspective on the existing literature, we establish a variety of new results including dual representations and extensions of surplus-invariant risk measures and structural results for surplus-invariant acceptance sets. We illustrate the power of the lattice approach by specifying our results to model spaces with a dominating probability, including Orlicz spaces, as well as to robust model spaces without a dominating probability, where the standard topological techniques and exhaustion arguments cannot be applied.

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