On law invariant coherent risk measures

By S. Kusuoka. 2001

742 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/212bc185f08a2ab4404e1c244ba852c20bca3024

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Citations in the corpus

Robust distortion risk measures (2022, background): “Furthermore, concave distortion risk measures span the class of law-invariant, coherent, and comonotone additive risk measures (Kusuoka, 2001).”
Seven Proofs for the Subadditivity of Expected Shortfall (2015, background): “The class of spectral riskmeasures in [2] can bewritten as a continuously weighted average of ES; see [37] and [26].”
Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements (2006, background): “Kusuoka (2001) and Acerbi (2004, pp. 180-182) show that all coherent risk measures that satisfy the two additional properties of comonotonic additivity and law invariance are also spectral measures.”
Optimal risk sharing under distorted probabilities (2008, background): “Keywords Distortion risk measures · Comonotonicity · Risk sharing · Pareto optimal allocations Mathematics Subject Classification (2000) 91B30 · 91B32 · 62P05”
RISK MEASURES ON ORLICZ HEARTS (2009, background): “…far, the most extensively studied cases have been L∞ over a probability space and L∞ over a measurable space; see, for instance, Delbaen (2000, 2002), Kusuoka (2001), Föllmer and Schied (2002a, 2002b, 2004), Frittelli and Rosazza Gianin (2005), Krätschmer (2005), Jouini, Schachermayer, and Touzi…”
A new integral for capacities (2009, neutral): “The studies of Kusuoka (2001) and Leitner (2005) assume an underlying additive probability distribution, while the underlying capacity here is typically non-additive.”
Measuring and Managing Credit Risk (2004, background): “Some literature exists on incorporating utility functions in risk measures (see, e.g., Acerbi, 2002; Bezard, 2002; or Kusuoka, 2001).”
Stochastic Orders and Risk Measures: Consistency and Bounds (2006, positive): “Similar results can be found in a series of papers by Ogryczak and Ruszczy´nski (1999,2001,2002).”
A REPRESENTATION RESULT FOR CONCAVE SCHUR CONCAVE FUNCTIONS (2005, background): “…literature (see Chong and Rice 1971) and a version of representation results more recently obtained for law-invariant convex or coherent risk measures in the mathematical finance literature (see Kusuoka 2001; Fritelli and Rosazza Gianin 2005; Rosazza Gianin 2002; Kunze 2003; Leitner 2005).”
Risk Measures and Robust Optimization Problems (2006, background): “Such risk measures were first discussed systematically by Kusuoka[53].”
Statistical estimation of composite risk functionals and risk optimization problems (2015, background): “The original result is presented in Kusuoka (2001) for risk measures defined on L∞(Ω,F, P), with an atomless probability space.”
Expected shortfall and beyond (2002, background): “It turned out (Kusuoka, 2001; Acerbi and Tasche, 2002) that ES from Definition 3.2 is just the smallest coherent and law invariant majorant of VaRα which had been already mentioned in Delbaen (1998).”
Properties of Distortion Risk Measures (2009, background): “They are also studied with a different approach by Kusuoka (2001) , who shows that a spectral measure can be associated to coherent risk measures that have two additional properties, law invariance and comonotone additivity (see Denneberg 1994 for the latter).”
The natural Banach space for version independent risk measures (2013, background): “[18] and (3) below) and results on continuity.”
Spectral measures of risk: A coherent representation of subjective risk aversion (2002, background): “[8].”