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.
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 not only integrates existing forms of time consistency , but also provides a comprehensive toolbox for analysis and synthesis of the concept of time consistency in decision making. In particular, it allows for in depth comparative analysis of (most of) the existing types of time consistency -- a feat that has not be possible before and which is done in the companion paper BCP2016] to this one. 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 . The form of the update rule introduced here is novel, and is perfectly suited for developing the unifying framework that is worked out in this paper. As an illustration of the applicability of our approach, we show how to recover almost all concepts of weak time consistency by means of constructing appropriate update rules.
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