Transcription of Optimization of Conditional V alue-at-Risk
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Optimization of Conditional V alue-at-Risk
(CVaR)ratherthanminimizingValue-at-Risk( VaR), ,alsocalledMeanExcessLoss,MeanShortfall, orTailVaR, ,brokerage rms,mutualfunds, , .edu,URL: . (VaR)hasaroleintheapproach,buttheemphasi sisonConditionalValue-at-Risk(CVaR),whic hisknownalsoasMeanExcessLoss,MeanShortfa ll, nitionwithrespecttoaspeci edprobabilitylevel ,the -VaRofaportfolioisthelowestamount suchthat,withprobability ,thelosswillnotexceed ,whereasthe -CVaRistheconditionalexpectationoflosses abovethatamount .Threevaluesof , nitionsensurethatthe -VaRisnevermorethanthe -CVaR, ,alongwithre-latedresources, ,approachestocalculatingVaRrelyonlineara pproximationoftheportfoliorisksandassume ajointnormal(orlog-normal)dis-tributiono ftheunderlyingmarketparameters,see,forin stance,Du eandPan(1997),Jorion(1996),Pritsker(1997 ),RiskMetrics(1996),Simons(1996),Beder(1 995),Stambaugh(1996).Also,historicalorMo nteCarlosimulation-basedtoolsareusedwhen theportfoliocontainsnon-linearinstrument ssuchasoptions(BucayandRosen(1999),Jorio n(1996),MauserandRosen(1999),Pritsker(19 97),RiskMetrics(1996),Beder(1995),Stamba ugh(1996)).
Optimization of Conditional V alue-at-Risk R. T yrrell Ro c k afellar 1 and Stanisla v Ury asev 2 A new approac h to optimizing or hedging a p ortfolio of nancial instrumen
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