Dynamic Coherent Acceptability Indices And Their Applications To Finance

In this paper, the authors present a theoretical framework for studying coherent acceptability indices in a dynamic setup. They study dynamic coherent acceptability indices and dynamic coherent risk measures, and they establish a duality between them. They derive a representation theorem for dynamic coherent risk measures in terms of so called dynamically consistent sequence of sets of probability measures. Based on these results, they give a specific construction of dynamic coherent acceptability indices. They also provide examples of dynamic coherent acceptability indices, both abstract and also some that generalize selected classical financial measures of portfolio performance.