One-parameter Families of Distortion Risk Measures

This paper introduces parametric families of distortion risk measures, investigates their properties, and discusses their use in risk management. Their derivation is based on Kusuoka's representation theorem of law invariant and comonotonically additive coherent risk measures. Our approach is to narrow down a tractable class of risk measures by requiring their comparability with the traditional expected shortfall. We make numerical comparison among them and propose a method of estimating the value of the distortion risk measures based on data. Their use and interpretation in risk management will also be discussed.