  We propose a robust risk measurement approach that minimizes the expectation
of overestimation plus underestimation costs. We consider uncertainty by taking
the supremum over a collection of probability measures, relating our approach
to dual sets in the representation of coherent risk measures. We provide
results that guarantee the existence of a solution and explore the properties
of minimizer and minimum as risk and deviation measures, respectively. An
empirical illustration is carried out to demonstrate the use of our approach in
capital determination.
