  Recently, financial industry and regulators have enhanced the debate on the
good properties of a risk measure. A fundamental issue is the evaluation of the
quality of a risk estimation. On the one hand, a backtesting procedure is
desirable for assessing the accuracy of such an estimation and this can be
naturally achieved by elicitable risk measures. For the same objective, an
alternative approach has been introduced by Davis (2016) through the so-called
consistency property. On the other hand, a risk estimation should be less
sensitive with respect to small changes in the available data set and exhibit
qualitative robustness. A new risk measure, the Lambda value at risk (Lambda
VaR), has been recently proposed by Frittelli et al. (2014), as a
generalization of VaR with the ability to discriminate the risk among P&L
distributions with different tail behaviour. In this article, we show that
Lambda VaR also satisfies the properties of robustness, elicitability and
consistency under some conditions.
