The use of fexible quantile-based measures in risk assessment

A new family of distortion risk measures GlueVaR is proposed in Belles-Sampera et al. (2014) to procure a risk assessment lying between those provided by common quantile-based risk measures. GlueVaR measures may be expressed as a combination of these standard risk measures. We show here that this relationship may be used to obtain approximations of GlueVaR measures for general skewed distribution functions using the Cornish-Fisher expansion. A subfamily of GlueVaR measures satisfies the tail-subadditivity property. An example of risk measurement based on real insurance claim data is presented, where implications of tail-subadditivity in the aggregation of risks are illustrated