In this paper, we propose a risk measurement approach that minimizes the expectation of sum between costs from capital determination overestimation and underestimation. We develop results that guarantee the existence of a solution , indicate properties that our risk measure fulfills, and characterize the resulting minimum cost as a deviation measure. We generalize this approach to a robust framework, where the minimization is over a supremum of expectations, based on a convex set of probability measures . We relate this robust approach with the dual representation of coherent risk measures. In a numerical example, we illustrate our approach for simulated and real financial data . Results indicate our approach leads to more parsimonious capital requirement determinations and reduces the mentioned costs  .
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 .
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In this paper, we propose a
We propose a robust
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capital determination
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develop
consider uncertainty by taking the supremum over alternative probability measures. We provide
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, indicate properties that our risk measure fulfills, and characterize the resulting minimum cost as a deviation measure. We generalize this approach to a robust framework, where the minimization is over a supremum of expectations, based on a convex set of probability measures
and explore the properties of minimizer and minimum as risk and deviation measures, respectively
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In a numerical example, we illustrate our approach for simulated and real financial data
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
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our approach leads
that our risk measures lead
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reduces
reduce
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. In addition, results point out advantages of our loss function over traditional approaches used in model selection