Spectral measures of risk: A coherent representation of subjective risk aversion

By C. Acerbi. 2002

407 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/979b28447145ce9a0dd2d623df3db7a1649fc573

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Citations in the corpus

How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics (2017, background): “ metrics [12, Chapter 4.7]. These risk metrics have a characterization in terms of Choquet integrals, which we now discuss with the help of additional terminology. Deﬁnition 1. A set function g : 2W ![0;1] is called monotone if g(A) g(B) for all A B W, and normalized if g(?)=0 and g(W)=1. If, in add”
Deviation Measures in Risk Analysis and Optimization (2002, positive): “Thus, the distribution function for the lower α-tail is obtained by truncating the distribution function from above at the α level and then rescaling so that the vertical range fits with [0, 1] instead of just [0, α].”
Two-sided coherent risk measures and their application in realistic portfolio optimization (2008, methodology): “As an application-oriented research and along a new derivation way, our new measure can be regarded as the improvement on preliminary coherent risk measures in Acerbi (2002), Fischer (2001, 2003) and as a variant of deviation measures in Rockafellar et al. (2006).”
Extremiles: A New Perspective on Asymmetric Least Squares (2018, background): “An often convenient, equivalent definition of ντ is as a spectral risk measure called expected shortfall (ES; Acerbi 2002).”
Robust distortion risk measures (2022, positive): “…0 < 𝑞 0 < 1 , where Φ and 𝜙 denote the standard normal distribution and its density, respectively; and the Tail Value-at-Risk (TVaR 𝛼 ), also called Expected Shortfall, at level 0 < 𝛼 < 1 (Acerbi, 2002) with In Section 4.1, we also consider the case of Value-at-Risk (VaR 𝛼 ), 0 < 𝛼 < 1 , a…”
Properties of Distortion Risk Measures (2009, background): “…concept of coherent risk measure and its defining properties, different sets of measures started to appear, each with distinctive properties: convex measures (see Föllmer and Shied 2002 or Fritelli and Rosazza 2002), spectral measures (Acerbi 2002) or deviation measures (Rockafellar et al. 2006a).”
Estimation of tail risk based on extreme expectiles (2016, neutral): “Journal of the Royal Statistical Society: Series B, Royal Statistical Society, 2018, 80 (2), pp.”
Optimal Financial Portfolios (2007, positive): “For more details on spectral risk measures and the linearization of the optimal portfolio problem, see Acerbi ( 2002 ), Acerbi and Simonetti ( 2002 ) and Acerbi ( 2004 ).”
Elicitable Risk Measures (2014, positive): “0 VaRu(F )du, α ∈ (0, 1) was proposed by Acerbi and Tasche (2002) as a valid alternative to VaR, with the advantage that it belongs to the class of coherent risk measures (see Artzner et al.”
Reward-Risk Portfolio Selection and Stochastic Dominance (2005, neutral): “Note that ρφ(X) = − ∫ 1 0 φ(t)F−1X (t) dt + ∫ 1 0 F−1X (t) dt = − ∫ 1 0 (φ(t)− 1) F−1X (t) dt, which is still a spectral measure, but the corresponding spectrum is not acceptable in the sense of Acerbi (2002) (see Acerbi and Simonetti 2002, Proposition 4.1).”