In the intense debate on risk measure properties, large attention has been recently devoted to elicitability. A statistical functional is elicitable, if it canbe written as the minimiser of an expected loss function; the mean, the quantileand the expectile are prominent examples. Elicitability is also relatedt o the idea of regression, indeed the loss function can be used to measure the “distance” between a given variable Y and a regression function. These concepts have been employed for fair valuation in actuarial mathematics, where the expected loss function is used to find a portfolio that is as close as possible to an insurance liability, while having a residual risk of zero. In this work we use elicitability to find the risk estimator that best approximatea financial loss in a context of model uncertainty. When the probability distribution of the loss is unknown, the risk measure is estimated based on (historical) data and takes different values depending on the realisation of the sample used. Our goal is to find the best strategy/risk measure estimator that also reflects the riskiness arising from distribution uncertainty. In particular, focusing on the family of location-scale distributions, we consider elicitable risk measures and different estimators, we study their properties and evaluate their accuracy.

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