Accuracy of L-moments approximation for spectral risk measures in heavy tail distributions

Abstract

This paper investigated the accuracy of linear-moment (L-moment) approximation for spectral risk measures (SRMs). The problem is considered in two cases of individual and aggregated loss measurements. The results showed that the absolute error of this approximation increases, in terms of a linear relation, when the loss goes to have a more heavy tail distribution. Therefore, due to the right skewed and heavy tail structure of the usual loss distributions in real word applications, using the L-moment approximation to estimate the SRMs leading to inaccurate estimation of spectral risk measures.

Subject Classification: (2010):

• 62P05
• 62P20

Keywords:

• Spectral risk measures
• Individual loss
• Aggregated loss
• L-moments
• Quantile function