On time consistency of dynamic risk and performance measures in discrete time

In this paper we provide a unified and flexible framework for study of the time consistency of risk and performance measures. The proposed framework integrates existing forms of time consistency as well as various connections between them. In our approach the time consistency is studied for a large class of maps that are postulated to satisfy only two properties -- monotonicity and locality. This makes our framework fairly general. The time consistency is defined in terms of an update rule -- a novel notion introduced in this paper. We design various updates rules that allow to recover several known forms of time consistency, and to study some new forms of time consistency.