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Recent advances in mathematical finance established linkages among several key concepts related to coherence, distorted risk measures, and information theory. The purpose of this paper is to extend these theoretical results for empirical applications in computational finance. First, we use a concentrated (dual) entropy approach to derive a computational algorithm for estimating the parameters of a distorted probability model associated with a coherent risk measure for a given sample of observed data. Second, we derive the asymptotic sampling properties of the estimated model parameters, which may be used to conduct classical hypothesis tests or to form other statistical inferences based on the estimated coherent risk measure. Third, we note that researchers may also require an estimate of the net loss distribution, and we propose an information theoretic procedure for jointly estimating the net loss probability model and the distorted probability distribution associated with a particular coherent risk measure.

Computation and asymptotic properties of estimated coherent risk measures