Conditional Value-at-Risk for General Loss Distributions

By R. Tyrrell Rockafellar, Stanislav Uryasev. 2002

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

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Citations in the corpus

Wireless Network Intelligence at the Edge (2018, methodology): “The right tail of the biased loss distribution can describe this, which has been investigated in mathematical finance using value-atrisk (VaR) and conditional-value-at-risk (CVaR) [143].”
Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management (2009, background): “(8) For each i and fixed x, the optimal solution set of min α∈R F i β (x, α) is a nonempty, closed and bounded interval (see Rockafellar and Uryasev 2000, 2002).”
A unified framework for stochastic optimization (2019, background): “…Ruszczy ́nski and Shapiro (2006) , which in turn uilds on what is now an extensive literature on risk measures n finance ( Rockafellar & Uryasev, 20 0 0; Kupper & Schachermayer, 0 09; Rockafellar & Uryasev, 20 02 for some key articles), with a eneral discussion in Rockafellar and Uryasev (2013) .”
Stability analysis of portfolio management with conditional value-at-risk (2007, background): “Rockafellar and Uryasev (2002) introduced a definition of the conditional value-at-risk (CVaR) measure for general distributions, including discrete distributions that exhibit discontinuities, and showed that CVaR is a continuous and convex function of the portfolio positions.”
An enhanced model for portfolio choice with SSD criteria: a constructive approach (2011, methodology): “, S} in (25) is – equivalent to the constraint belonging to Ji in (22), if |Ji| = i; – redundant if |Ji| 6= i.”
Tilted Empirical Risk Minimization (2020, background): “Finally, we show that TERM is related to superquantile -based objectives, which aim to minimize speciﬁc quantiles of the individual losses, also known as Value-at-Risk (VaR) in optimization and ﬁnance literature [52, 53].”
Risk Aversion in Inventory Management (2007, background): “When the underlying distribution is discrete, a more general definition of CVaR ( see [24, 25]) is as follows: Definition 2.”
Capital Allocation to Business Units and Sub-Portfolios: the Euler Principle (2007, background): “ES is quite straightforward. 5The denotation “Expected Shortfall” was proposed by Acerbi and Tasche (2002). A common alternative denotation is “Conditional Value-at-Risk (CVaR)” that was suggested by Rockafellar and Uryasev (2002). 9 3.4 Risk measures for sample data In most circumstances, portfolio”
Copulas: A Review and Recent Developments (2006, background): “Rockafellar, R.; Uryasev, S. Conditional value-at-risk for general loss distributions.”
Optimization with Stochastic Dominance Constraints (2003, background): “Other stochastic optimization models involving general risk functionals were considered by [35, 13, 27, 29].”
Financial prediction with constrained tail risk (2007, background): “One of these is the notion of a coherent risk measure, an example of which is CVaR (Rockafellar and Uryasev, 2000, 2002), constituting a computationally attractive alternative to VaR.”
Stochastic dominance analysis of Asian hedge funds (2008, methodology): “On the other hand, studies have applied the Value-at-Risk (VaR) and conditionalVaR (CVaR) (see for example, Jorion, 2000; Rockafellar and Uryasev, 2000, 2002; Alexander and Baptista, 2002, 2004) methodology to hedge funds.”
Robust portfolio selection under downside risk measures (2009, background): “…measure and Conditional VaR (CVaR) which has gained much attention in recent years due to its convenience in computation and its coherent properties for measuring risk (Artzner et al. 1999, Rockafellar and Uryasev 2000, 2002, Acerbi and Tasche 2002, Testuri and Uryasev 2003, Bertsimas et al. 2004).”
Coherent measures of risk in everyday market practice (2007, methodology): “The problem of finding efficient optimization routines for ES α was however elegantly solved by Pflug ( 2000 ), and Rockafellar and Uryasev ( 2000 , 2002 ) who mapped it onto the equivalent problem of finding the minima of the functional with <inline-graphic xmlns:xlink="http://www.”