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

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 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 Law invariant risk measures onL∞(ℝd)

2011 ◽  
Vol 28 (3) ◽  
pp. 195-225 ◽  
Author(s):  
Ivar Ekeland ◽  
Walter Schachermayer
Keyword(s):  
Risk Measures ◽  
Law Invariant Risk Measures

scholarly journals INF-Convolution of Risk Measures on Rearrangement Invariant Spaces

2021 ◽  
Author(s):  
Shengzhong Chen
Keyword(s):  
Risk Measures ◽  
Model Space ◽  
Continuity Condition ◽  
Individual Risk ◽  
Risk Allocation ◽  
Fatou Property ◽  
Economic Agents ◽  
Research Areas ◽  
Optimal Capital ◽  
Invariant Spaces

The problem of optimal capital and risk allocation among economic agents, has played a predominant role in the respective academic and industrial research areas for decades. Typically as risk occurs in face of randomness the risks which are to be measured are identified with real-valued random variables on some probability space (Ω, F, P). Consider a model space X , and n economic agents with initial endowments X1, · · · , Xn ∈ X who assess the riskiness of their positions by means of law-invariant convex risk measures ρi : X → (−∞,∞]. In order to minimize total and individual risk, the agents redistribute the aggregate endowment X = X1 + · · · + Xn among themselves. An optimal capital and risk allocation Y1, · · · , Yn satisfies Y1 + · · · + Yn = X and ρ1(Y1) + · · · + ρ(Yn) = inf nXn i=1 ρi(Xi) : Xi ∈ X , i = 1, . . . , n, and Xn i=1 Xi = X o , (0.1) where n i=1ρi(X) = inf nPn i=1 ρi(Xi) : Xi ∈ X , i = 1, . . . , n, and Pn i=1 Xi = X o is the inf-convolution of ρ1, ..., ρn. In 2008, Filipovi´c and Svindland proved that if X is an L p (P) for some 1 ≤ p ≤ ∞ and ρi satisfy a suitable continuity condition (i.e. Fatou property), then Problem (0.1) always admits a solution. To reflect the fact of randomness of risk, we should consider the model space X chosen for risk evaluations to be as general as possible. The main contribution of this thesis is Theorem 4.10 has been published in [9]. It extends Filipovi´c and Svindland’s result from L p spaces to general rearrangement invariant (r.i.) spaces.

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