Coherent risk measures

By Freddy Delbaen. 2000

365 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/545d4de9b1477120628b3745c7fb37c61a9884a3

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Citations in the corpus

Coherent measures of risk in everyday market practice (2007, background): “The general representation of CRMs is well known (Artzner et al. 1999, Delbaen 2000).”
Dynamic risk measures (2010, methodology): “For a comprehensive presentation of the theory of static coherent and convex risk measures, we refer to Delbaen [15] and Föllmer and Schied [24, Chap.”
DYNAMIC INDIFFERENCE VALUATION VIA CONVEX RISK MEASURES (2007, background): “Finally Q can be chosen convex and closed in L1 as in Delbaen (2000).”
Coherent and convex risk measures for bounded cadlag processes (2003, background): “The notion of a coherent risk measure was introduced in [ADEH1] and [ ADEH2 ], where it was also shown that every coherent risk measure on the space of all random variables on a finite probability space can be represented as a supremum of linear functionals.”
Risk Capital allocation by coherent risk measures based on one-sided moments (2003, background): “For a deeper study of the connections between the theory of convex games and coherent risk measures we refer to Delbaen (2002).”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “However, the value-at-risk has been criticized by certain authors, in particular because it fails to be a coherent risk measure, as defined in [10].”
Ambiguous chance constrained problems and robust optimization (2006, background): “Ruszczynski and Shapiro [38] show the equivalence between minimax stochastic programming and minimizing a convex risk measure [ 2 , 24] of the second-stage cost.”
Operational Risk Quantification Using Extreme Value Theory and Copulas: From Theory to Practice (2009, neutral): “However, Delbaen (2002) shows that any coherent risk measure ρ which is dependent on the distribution function of the risks and for which ρ ≥ V aRα has to satisfy ρ ≥ ESα, where ES (Expected Shortfall) requires the existence of the first moment (i.e. ξ 1).”
THE CANONICAL MODEL SPACE FOR LAW‐INVARIANT CONVEX RISK MEASURES IS L1 (2012, background): “Convex risk measures are best known on L1. Indeed, Artzner et al. [1] introduced the seminal axioms of coherence, which then were further generalised to the convex case by F ollmer and Schied [6] and Frittelli and Rosazza-Gianin [8], on L1. However, there is a growing mathematical nance literature ”