Dynamic coherent acceptability indices and their applications to finance, Mathematical Finance

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