  In this paper we present a theoretical framework for studying coherent
acceptability 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 dynamically 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.
