On distortion functionals

SUMMARY Distorted measures have been used in pricing of insurance contracts for a long time. This paper reviews properties of related acceptability functionals in risk management, called distortion functionals. These functionals may be characterized by being mixtures of average values-at-risk. We give a dual representation of these functionals and show how they may be used in portfolio optimization. An iterative numerical procedure for the solution of these portfolio problems is given which is based on duality.