Coherent Risk Measures on General Probability Spaces

By Freddy Delbaen. 2002

842 citations recorded by the source corpus.

Subfields: Economics and Econometrics, General Decision Sciences, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/9fcdab738248a0fca4157edab8dce64d2d1aab55

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In General Decision Sciences

In Management Science and Operations Research

Citations in the corpus

Backtesting for Risk-Based Regulatory Capital (2004, methodology): “This definition, in which a “risk” is a random variable defined on a given probability space, follows the terminology of Artzner et al. (1999) and Delbaen (2000).”
VALUATIONS AND DYNAMIC CONVEX RISK MEASURES (2007, background): “…et al. 2004, 2006; Klöppel and Schweizer 2007), we shall instead speak of a valuation,2 1 See Deprez and Gerber (1985), Artzner et al. (1997, 1999), Delbaen (2000, 2002, 2003), Jaschke and Küchler (2001), Föllmer and Schied (2002a, b), Frittelli and Rosazza Gianin (2002, 2005), and Cherny…”
Coherent measures of risk in everyday market practice (2007, background): “3 THE OBJECTIVIST PARADIGM The general representation of CRMs is well known (Artzner et al. 1999; Delbaen 2000).”
n-MONOTONE EXACT FUNCTIONALS (2008, background): “nd generalise a number of notions in the literature, such as coherent lower previsions (Walley [20]), exact cooperative games (Schmeidler [18]) and coherent risk measures (Artzner et al. [2], Delbaen [9]). Coherent lower previsions, mainly due to Walley [20], are among the most interesting uncertain”
Entropic Value-at-Risk: A New Coherent Risk Measure (2012, background): “[4] for the discrete case, and then extended for a general case by Delbaen [5].”
Coherent and convex risk measures for bounded cadlag processes (2003, background): “In [FS1] and [FS2] the more general concept of a convex risk measure was introduced and representation results of [ De1 ] were generalized to convex risk measures on the space of all bounded variables on a general probability space.”
MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS (2013, background): “Define the set-valued risk measure ρZ (X) = ⋂ Z∈Z E(X̌Z) EZ ,(4.2) which is similar to the classical dual representation of coherent risk measures, see Delbaen (2002) and also corresponds to the (Q, w)-representation of risk measure in conical models from Hamel et al. (2011, th. 4.2) that is…”
RISK MEASURES ON ORLICZ HEARTS (2009, methodology): “In Delbaen (2002) and Cheridito et al. (2006) coherent and convex monetary risk measures on L0 are investigated and it is shown that to have non-trivial examples, one has to allow them to take values at least in (−∞, ∞].”
Time consistent dynamic risk processes (2009, background): “For the particular case of coherent dynamic risk measures (i.e. when the penalty is identically equal to 0 on Q) the result was proved by Delbaen [9].”
A REPRESENTATION RESULT FOR CONCAVE SCHUR CONCAVE FUNCTIONS (2005, background): “Finally, the concepts of law-invariant coherent measure of risk and of law-invariant convex measure of risk are introduced in mathematical finance (see Delbaen 2001, 2002, and Föllmer and Schied 2002 for a review).”
Risk-averse dynamic programming for Markov decision processes (2010, background): “Particularly relevant for us are the duality theory [1, 10, 14, 16, 17, 34, 43, 45, 46], and the theory of conditional and dynamic risk measures [2, 8, 11, 15, 18, 19, 28, 38, 48, 40, 45, 47].”
Bayesian Robust Optimization for Imitation Learning (2020, background): “Conditional Value at Risk CVaR is a coherent risk measure [15] that is also commonly referred to as average value at risk, expected tail risk, or expected shortfall.”
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].”