Kaynar, B.

function distribution problem measure portfolio decision value risk measure algorithm decision maker vector optimization disutility return model maker disutility function risk measures lemma multivariate result vector x disutility functions solution decision makers table section computation times management cvar values distributions sabanci university proof markowitz approach value-at-risk relation paper ax x 1 matrix risk management model michelot range objective function objective distribution function definition covariance matrix vector y asset increase computation programming rockafellar quadprog representation michelot algorithm portfolio optimization number deviation uryasev loss functions point sequence xk x university multivariate t loss function class step algorithm optimization problem sample carlo monte monte carlo simulation cvar measures cv ar simulation world loss function f observation embrecht