Law Invariant Risk Measures Have the Fatou Property

By Elyès Jouini, W. Schachermayer, Nizar Touzi. 2005

323 citations recorded by the source corpus.

Subfields: Applied Mathematics, Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/e27fd513a4a7d18f86d9cca2aef90423cf6a7da7

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In Applied Mathematics

In Economics and Econometrics

In Management Science and Operations Research

Citations in the corpus

The natural Banach space for version independent risk measures (2013, background): “Further properties and importance of spectral risk measures A well known and essential representation of risk measures was elaborated by Kusuoka in [18] (see [17] for the statement presented below).”
Law invariant convex risk measures for portfolio vectors (2006, background): “14), which leads to a Kusuoka type representation as in (1.1) and also to a distortion type repesemtation as in (1.4) (see Dana (2005), Föllmer and Schied (2004), Carlier and Dana (2003)).”
RISK MEASURES ON P(R) AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION (2014, unknown): “Jouini, Schachermayer and Touzi (2006) [14], in the convex case, and Svindland (2010) [16] in the quasi-convex case, showed that every law invariant risk measure is already weakly lower semicontinuous.”
RISK MEASURES FOR NON‐INTEGRABLE RANDOM VARIABLES (2009, background): “The continuity from below is now a consequence of weak compactness as can be seen from Jouini, Schachermayer, and Touzi (2006).”
Consistent risk measures for portfolio vectors (2006, unknown): “(44) Proof: By a recent result of Jouini et al. (2005) law invariant risk measures have the Fatou property.”
Risk Measures and Robust Optimization Problems (2006, result): “The condition of continuity from above can in fact be dropped: every law-invariant convex risk measure is automatically continuous from above, as was shown very recently by Jouini et al.[48].”
Representation results for law invariant time consistent functions (2009, background): “[26] that any law invariant convex risk measure ρ0 automatically has the Fatou property.”
On the optimal risk allocation problem (2006, background): “For some of the large number of references see Leland (1980), Chavallier and M¨uller (1994), and Barrieu and El Karoui (2002a, 2002b, 2003, 2004, 2005), Dana and Scarsini (2005), Chateauneuf, Dana, and Tallon (2000), Gerber (1979), Landsberger and Meilijson (1994), Denault (2001), Dana and Meilijson”
COHERENCE AND ELICITABILITY (2013, background): “They are expectiles which were first introduced by Newey and Powell (1987). The elicitability of expectiles is a simple corollary of their definition.”
Dual characterization of properties of risk measures on Orlicz hearts (2008, unknown): “It has been noted before that AVaR can be used as a building block to construct other risk measures; see for instance, Kusuoka (2001), Acerbi (2002, 2004), Föllmer and Schied (2004), Frittelli and Rosazza Gianin (2005), Jouini et al. (2005), Leitner (2005), Dana (2005), or Jouini et al. (2006).”
RISK MEASURES ON ORLICZ HEARTS (2009, background): “In this setting, and expressed in discounted units, the main structural results are that every monetary risk measure ρ can be written as ρ(X) = inf {m ∈ R : X + m ∈ C} ,(1.1) We thank Freddy Delbaen, Andreas Hamel, Michael Kupper and Alexander Schied for fruitful discussions and helpful comments.”
MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS (2013, background): “Its symmetric variant Ǩ is the solvency cone, while the dual cone K ′ contains all consistent price systems, see Kabanov and Safarian (2009); Schachermayer (2004). Formally, K is a random closed set with values being cones.”
OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS (2008, background): “The key-ingredient is the quantile representation of Kusuoka [32] which is further extended in [22], [25] and [29].”
OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY‐BASED PRICING (2007, methodology): “ց E P-a.s. =⇒ u(En) ց u(E) and En ր E P-a.s. =⇒ u(En) ր u(E). The terminology “Lebesgue Continuity” has been motivated by similar terminology for utility functions deﬁned on L∞, which can be found in [JST06]. Corollary 5.3 Deﬁne uE(B) = uE+B. Then uE(B) satisﬁes the properties (i)-(iv) of Propositio”