A robust approach for minimization of risk measurement errors

We propose a robust risk measurement approach that minimizes the expectation of sum between costs from overestimation and underestimation. We consider uncertainty by taking the supremum over alternative probability 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. We relate this robust approach with the dual representation of coherent risk measures. Moreover, we suggest the use of our loss function in the verification of risk estimation or forecasting quality. Two empirical illustrations are carried out to demonstrate the use of our approach in the capital determination and selection of risk prediction models. Results indicate that our risk measures lead to more parsimonious capital requirement determinations and reduce the mentioned costs. In addition, results point out advantages of our loss function over traditional approaches used in model selection.