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Communication systems and network technologies
Published in Kennis Chan, Future Communication Technology and Engineering, 2015
By the above definition, VaRα(X) is a left α quantile of the random variable X. For a given time horizon t and confidence level α, the VaR of a portfolio is the potential loss in the portfolio’s market value over the time horizon t that is exceeded with probability 1−α. VaR has become a popular risk measure for risk management both for the purpose of reporting and measurement of capital adequacy. Despite its wide acceptance, it is not a coherent risk measure. A coherent risk measure should satisfy the axioms of translation invariance, subaddivity, positive homogeneity, and monotonicity. Unfortunately, VaR lacks subadditivity.
Risk quantification for life-cycle management of infrastructure considering the effect of maintenance behavior
Published in Jaap Bakker, Dan M. Frangopol, Klaas van Breugel, Life-Cycle of Engineering Systems, 2017
Another coherent risk measure is Conditional Value at Risk (CVaR). The definition of CVaR is given as CVaR1−α(X)=1α∫0αVaR1−l(X)dk
Refinements of Kusuoka representations on L ∞
Published in Optimization, 2022
A real-valued functional is called a coherent risk measure, if it satisfies the following axioms: (A1) If and , -a.s., then .(A2) For all and all , (A3) If and , then .(A4) If , and , then .
Risk-averse multi-stage stochastic programming to optimizing vaccine allocation and treatment logistics for effective epidemic response
Published in IISE Transactions on Healthcare Systems Engineering, 2022
Xuecheng Yin, İ Esra Büyüktahtakın
Conditional value-at-risk (CVaR) is a coherent risk measure that can be used in an optimization model without losing convexity (Rockafellar & Uryasev, 2002). Therefore, many previous studies considered mean-risk models with CVaR in stochastic programming models (Ahmed, 2006; Miller & Ruszczyński, 2011; Rockafellar & Uryasev, 2002; Schultz & Tiedemann, 2006). CVaR-based mean-risk stochastic programming has been studied in various applications, such as supply chain management (Alem & Morabito, 2013), reverse logistic network design problem (Soleimani & Govindan, 2014), solid waste management system (Dai et al., 2014), water resources allocation (Zhang et al., 2016), and forestry invasive species control planning (Bushaj et al., 2020, 2021).
Risk-averse two-stage distributionally robust optimisation for logistics planning in disaster relief management
Published in International Journal of Production Research, 2023
Duo Wang, Kai Yang, Lixing Yang
Given a confidence level α, the CVaR of a random variable Z, denoted by , is defined as where represents the positive part of the real number a. As a measure of risk, CVaR captures a wide range of risk preferences and exhibits some better properties than VaR. For instance, Zhu and Fukushima (2009) showed that CVaR is a coherent risk measure, which is transition-equivariant, positively homogeneous, convex, and monotonic. Moreover, compared to VaR criterion, CVaR emphasises the average level of excess losses and can reduce the unreliability aspect of risk variability.