A risk measure that optimally balances capital determination errors. (arXiv:1707.09829v1 [q-fin.RM])

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.