CVaR (superquantile) norm: Stochastic case

Mafusalov, Alexander; Uryasev, Stan

doi:10.1016/j.ejor.2015.09.058

Cited by 16 publications

(8 citation statements)

References 32 publications

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“…For methods of numerical estimation of the CVaR, see the works by Chernozhukov and Umantsev (2001) and Chun et al (2012). For more recent studies, applications and investigations of the ES in various models, see in particular the works by Drapeau et al (2014), Ivanov (2018), Kalinchenko et al (2012) and Mafusalov and Uryasev (2016).…”

Section: Resultsmentioning

confidence: 99%

A Credit-Risk Valuation under the Variance-Gamma Asset Return

Иванов

2018

Risks

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This paper considers risks of the investment portfolio, which consist of distributed mortgages and sold European call options. It is assumed that the stream of the credit payments could fall by a jump. The time of the jump is modeled by the exponential distribution. We suggest that the returns on stock are variance-gamma distributed. The value at risk, the expected shortfall and the entropic risk measure for this portfolio are calculated in closed forms. The obtained formulas exploit the values of generalized hypergeometric functions.

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Section: Resultsmentioning

confidence: 99%

A Credit-Risk Valuation under the Variance-Gamma Asset Return

Иванов

2018

Risks

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“…It can be noted that superquantiles are fundamental building blocks for estimates of risk in finance [64] and engineering [65]. In finance, the superquantile has various names, such as expected tail loss [66], conditional value-at-risk (CVaR) [67][68][69][70] or tail value-atrisk [71], average value at risk [72], expected shortfall [73,74]. Subquantile is not such a widespread concept.…”

Section: Linear Form Of Quantile-oriented Sensitivity Indices-contrasmentioning

confidence: 99%

Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

Kala

2021

Symmetry

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The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance.

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“…CVaRα -norm is the expectation of − α largest absolute values of X. The CVaRα -norm for the deterministic case was introduced in [8] and for the stochastic case in [7]. CVaRα-norm satis es the following standard properties:…”

Section: Cvar α -Norm Of Random Variablesmentioning

confidence: 99%

Fitting heavy-tailed mixture models with CVaR constraints

Pertaia

Uryasev

2019

Dependence Modeling

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Standard methods of fitting finite mixture models take into account the majority of observations in the center of the distribution. This paper considers the case where the decision maker wants to make sure that the tail of the fitted distribution is at least as heavy as the tail of the empirical distribution. For instance, in nuclear engineering, where probability of exceedance (POE) needs to be estimated, it is important to fit correctly tails of the distributions. The goal of this paper is to supplement the standard methodology and to assure an appropriate heaviness of the fitted tails. We consider a new Conditional Value-at-Risk (CVaR) distance between distributions, that is a convex function with respect to weights of the mixture. We have conducted a case study demonstrating e˚ciency of the approach. Weights of mixture are found by minimizing CVaR distance between the mixture and the empirical distribution. We have suggested convex constraints on weights, assuring that the tail of the mixture is as heavy as the tail of empirical distribution.

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CVaR (superquantile) norm: Stochastic case

Cited by 16 publications

References 32 publications

A Credit-Risk Valuation under the Variance-Gamma Asset Return

A Credit-Risk Valuation under the Variance-Gamma Asset Return

Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

Fitting heavy-tailed mixture models with CVaR constraints

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