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Buffered environmental contours
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
The approximations made by FORM and SORM can sometimes be too crude and ignore serious risks. Therefore, we will consider the buffered failure probability, introduced by Rockafellar & Royset (2010) as an alternative to the failure probability. This concept relates closely to the conditional value-at-risk (also called expected shortfall, average value-at-risk or expected tail loss), which is a notion frequently used in mathematical finance and financial engineering, see Pflug (2000), Rockafellar (2007) as well as Rockafellar & Uryasev (2000).
Communication systems and network technologies
Published in Kennis Chan, Future Communication Technology and Engineering, 2015
Another informative measure of risk is the Expected Shortfall (ES), which is also known as Mean Excess Loss or Tail VaR. ES is a more consistent measure of risk since it is subaddivity and convex. Next, we give a formal definition of ES.
Optimal portfolio choice for ship leasing investments
Published in Maritime Policy & Management, 2019
Carisa K.W. Yu, Tsz Leung Yip, Siu Kai Choy
Although VaR is a popular measure of risk, it has its limitations. One is its lack of sub-additivity. For example, the VaR of a portfolio with two or more assets may be greater than the sum of the VaR values of these constituent assets. As pointed out by Acerbi and Tasche (2002), managing risk using VaR may fail to stimulate diversification. Also, VaR is non-convex and non-smooth (Artzner et al. 1999). Moreover, VaR does not take into account the severity of an incurred damage event. Thus, another more preferable measure of risk, Conditional Value-at-Risk (CVaR), was introduced (Artzner et al. 1997; Rockafellar and Uryasev 2000). CVaR can be defined as the expected loss given that the loss is larger than or equal to VaR at a given confidence level. It is also variously referred to as the expected shortfall, mean excess loss, or tail VaR. As a measure of risk in the portfolio optimization problem, CVaR has superior properties to and computational advantages over VaR (Rockafellar and Uryasev 2002). Compared to VaR, CVaR is coherent, more consistent, and more stable with respect to the choice of confidence level.
Peaks Over Thresholds Modeling With Multivariate Generalized Pareto Distributions
Published in Technometrics, 2019
Anna Kiriliouk, Holger Rootzén, Johan Segers, Jennifer L. Wadsworth
The expected shortfall is defined as the expected loss given that a particular VaR threshold has been exceeded. Under the GP model, and provided γ < 1, it is given by Asymptotic theory suggests that a univariate GP model fit directly to ∑jaj(Yt, j − uj) or the implied GP(∑jajσj, γ) model obtained from the multivariate fit could be used. An advantage of using the GP(∑jajσj, γ) model derived from the multivariate fit is reduced uncertainty, combined with consistent estimates across different portfolio combinations.
Optimal budget allocation for stochastic simulation with importance sampling: Exploration vs. replication
Published in IISE Transactions, 2021
The stochastic simulation model is also called nested simulation, and it has been used to obtain financial portfolio risk measurements such as Value-at-Risk (VaR) and expected shortfall in the literature (Gordy and Juneja, 2010; Lan et al., 2010; Broadie et al., 2011). VaR is the quantile estimation of risk factors given the probability of loss. Its expected shortfall estimates the tail expectation that quantifies the actual loss amount when the large loss happens. In this way it complements a VaR that ignores the loss distribution beyond the quantile (Gordy and Juneja, 2010). The risk factors are drawn in the outer step and the loss is evaluated using the inner step simulation.