this issue
previous article in this issuenext article in this issue

Document Details :

Title: Analytical Bounds dor Two Value-at-Risk Functionals
Author(s): HÜRLIMANN, W.
Journal: ASTIN Bulletin
Volume: 32    Issue: 2   Date: November 2002   
Pages: 235-265
DOI: 10.2143/AST.32.2.1028

Abstract :
Based on the notions of value-at-risk and conditional value-at-risk, we consider two functionals, abbreviated VaR and CVaR, which represent the economic risk capital required to operate a risky business over some time period when only a small probability of loss is tolerated. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). This result is used to bound the VaR and CVaR functionals by determining their maximal values over the set of all loss and profit functions with fixed first few moments. The evaluation of CVaR for the aggregate loss of portfolios is also discussed. The results of VaR and CVaR calculations are illustrated and compared at some typical situations of general interest.