Optimization of conditional value-at risk

By R. Tyrrell Rockafellar, Stanislav Uryasev. 2000

6,922 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/58444c142b6ea5c71a435cac7a0b4c66d6c68869

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Citations in the corpus

Credit risk optimization with Conditional Value-at-Risk criterion (2001, methodology): “First, we present the minimum CVaR approach [18].”
Risk-Averse Bayes-Adaptive Reinforcement Learning (2021, background): “CVaR may also be defined as the expected value under a perturbed distribution using its dual representation [34, 37]”
Portfolio Theory: As I Still See It (2010, background): “…says that choice is, in a certain sense, a continuous function of probabilities p1, . . . , pn. 3 CVaR can also be derived from basic assumptions about desirable risk measures, namely that the risk measure be coherent in the sense provided by Pflug (2000); see also Rockafellar & Uryasev (2000).”
Equilibrium With Investors Using a Diversity of Deviation Measures (2007, positive): “These criticisms have led to the study of other measures of deviation which might be adopted as substitutes, for instance ones based in one way or another on conditional value-at-risk (Rockafellar and Uryasev, 2000; Rockafellar and Uryasev, 2002).”
Higher moment coherent risk measures (2007, background): “Example 1.1 (Conditional Value-at-Risk): A famous special case of (1) is the optimization formula for Conditional Value-at-Risk (Rockafellar and Uryasev 2000, 2002): CVaR ðX Þ ¼ min 2R þ ð1 Þ 1EðX Þþ, 05 51, ð2Þ where ðXÞ ¼ maxf X, 0g, and function ðXÞ ¼ ð1 Þ 1 EðXÞþ evidently satisfies the…”
Dual-channel supply chain pricing decisions with a risk-averse retailer (2014, methodology): “…as follows (Rockafellar and Uryasev 2000): CVaRg prð Þ ¼ E pr pr vg prð Þj½ : To simplify the computation, we will use the following equivalent definition (Rockafellar and Uryasev 2000): CVaRg prð Þ ¼ max v2R vþ 1 g E min pr v; 0ð Þ½ : Assuming that the manufacturer produces a single product…”
A Bilevel Stochastic Programming Approach for Retailer Futures Market Trading (2009, background): “Risk aversion is also incorporated by limiting the volatility of the expected profit through the conditional value-at-risk (CVaR) [17].”
Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization (2002, methodology): “Rockafeller and Uryasev [2000] show that optimizing ) (ω Φ is equivalent to optimizing ) , ( β ω F (see Appendix D for proof).”
Quantile cointegrating regression (2009, methodology): “A widely used coherent risk measure is the conditional value at risk1 (CVaR) (Rockafellar and Uryasev (2000)) (or, in di¤erent names, Expected Shortfall, Acerbi and Tasche (2002); tail conditional expectation, Artzner, Delbaen, Eber, and Heath (1999)).”
RAIL: Risk-Averse Imitation Learning (2017, methodology): “Rockafellar and Uryasev (2000) showed that if the distribution of the risk variable Z be normal, CV aR α ( Z ) = µ Z + a ( α ) σ Z , where a ( α ) is a constant for a given α , µ Z and σ Z are the mean and standard deviation of Z .”
The fundamental risk quadrangle in risk management, optimization and statistical estimation (2013, methodology): “This formula, in which C + V(X − C) is minimized over C , generalizes a rule in [5,6], for VaR–CVaR computations.”
Data-driven chance constrained stochastic program (2015, background): “…constraints (1b), previous research identiﬁes the special cases in which chance constraints are convex (see, e.g., [9,38], and [8]), and, for the general cases in which chance constraints are nonconvex, provides convex conservative approximations and relaxations (see, e.g., [11,32,39], and [1]).”
Nonparametric Return Distribution Approximation for Reinforcement Learning (2010, methodology): “As a representative example, in this section we develop an explicit formulations of a SARSA-learning-type approach with Conditional Value at Risk (CVaR) (Rockafellar & Uryasev, 2000; Kashima, 2007) as the evaluation criterion, on the basis of the particle distributions for the approximation.”
Stable distributions in the Black–Litterman approach to asset allocation (2007, methodology): “Notice that for elliptical distributions, following Embrechts,Lindskog and McNeil (2003) [9] and Stoyanov, Samorodnitsky, Rachev and Ortobelli (2004) [35], the CV aR of portfolio returns is expressed as For detailed description of CV aR see for example Rockafeller and Uryasev (2000) [33] and for α-s”