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In this paper we provide a flexible framework allowing for a unified study oftime consistency of risk measures and performance measures (also known asacceptability indices). The proposed framework not only integrates existingforms of time consistency, but also provides a comprehensive toolbox foranalysis and synthesis of the concept of time consistency in decision making.In particular, it allows for in depth comparative analysis of (most of) theexisting types of time consistency -- a feat that has not be possible beforeand which is done in the companion paper [BCP2016] to this one. In our approachthe time consistency is studied for a large class of maps that are postulatedto satisfy only two properties -- monotonicity and locality. The timeconsistency is defined in terms of an update rule. The form of the update ruleintroduced here is novel, and is perfectly suited for developing the unifyingframework that is worked out in this paper. As an illustration of theapplicability of our approach, we show how to recover almost all concepts ofweak time consistency by means of constructing appropriate update rules.

A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time