A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time

In this paper we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures, also known as acceptability indices. The proposed framework integrates existing forms of time consistency. 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. The time consistency is defined in terms of an update rule – a novel notion introduced in this paper. As an illustration of the usefulness of our approach, we show how to recover almost all concepts of weak time consistency by means of constructing various update rules.