Putting order in risk measures

By Marco Frittelli, Emanuela Rosazza Gianin. 2002

759 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/d068ad58ccb622f336f029f51dfcbce73d7058bd

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Citations in the corpus

On the Extension of the Namioka-Klee Theorem and on the Fatou Property for Risk Measures (2009, methodology): “applications (see for example, [ FR02 ], [FS07], [RK08]).”
Risk Measures and Robust Optimization Problems (2006, methodology): “This theory was initiated by P. Artzner, F. Delbaen, J. Eber, and D. Heath in their seminal paper[3] and further developed by Carlier and Dana[11], Delbaen[20,21], Föllmer and the author[33–36], Frittelli and Rosazza Gianin[37,38], Heath[43], Heath and Ku[44], and Kusuoka[53], to mention only a few.”
TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION (2010, neutral): “Ruszczynski [29]). An important extension is based on the relaxation of the positive homogeneity and subadditivity property into the weaker convexity property leading to the class of convex risk measures (see F˜ollmer and Schied [13], Fritelli and Gianin [ 15 ]).”
A decision-theoretic foundation for reward-to-risk performance measures (2012, background): “According to Ortobelli et al. (2005) (see also Szegö, 2002; Frittelli and Gianin, 2002), positive homogeneity is a sufficient (but not a necessary) condition to add to convexity in order to obtain sublinearity (=coherence) à la Artzner et al. (1999).”
Law invariant convex risk measures (2005, methodology): “Translation invariance: we recall from [ 9 ] that for any convex risk measure (ti) is equivalent to the property: p (c) = —c for any c G M. Hence we need only to show this last property.”
Properties of Distortion Risk Measures (2009, background): “Accordingly, they propose relaxing the conditions of positive homogeneity and sub-additivity to convexity (see also Fritelli and Rosazza 2002 ).”
Risk measuring under model uncertainty (2010, background): “This notion has been extended to general probability spaces [12] and then to the convex case ([21] and [22]).”
Convex risk measures and the dynamics of their penalty functions (2006, background): “Such representations for conditional risk measures were discussed in Riedel [18], Arztner et al. [2], Detlefsen [10], Detlefsen and Scandolo [11], Frittelli and Rosazza Gianin [15], Bion-Nadal [3], [4], Cheridito et al. [6], Burgert [5], and Klöppel and Schweizer [16].”
AN OLD‐NEW CONCEPT OF CONVEX RISK MEASURES: THE OPTIMIZED CERTAINTY EQUIVALENT (2007, background): “More recently, F˜ollmer and Schied [15], and Fritelli and Gianin [ 14 ] proposed to extend the concept coherent risk measure by relaxing the subadditivity and positive homogeneity conditions1 with the”
OPTIMAL CAPITAL AND RISK TRANSFERS FOR GROUP DIVERSIFICATION (2007, background): “Convex risk measures have been the topic in [1, 10, 16, 18, 19, 20, 22].”
VALUATIONS AND DYNAMIC CONVEX RISK MEASURES (2007, methodology): “By duality, the original functions πτ can be expressed as πτ (K) = inf λ {λ · K + π̃τ (λ)};(3.1) compare with the equation (1.2) above, as in Föllmer and Schied (2002a), and Frittelli and Gianin (2002).”
Time consistent dynamic risk processes (2009, background): “The notion of risk measure has been extended to the convex case by Föllmer and Schied [14,15] and Frittelli and Rosaza Gianin [17], and then to a conditional setting by Detlefsen and Scandolo [11] and Bion-Nadal [4].”