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 .
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 .
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unified and flexible framework for study of the
flexible framework allowing for a unified study of
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measures
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, also known as acceptability indices
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as well as various connections between them
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This makes our framework fairly general.
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We design various updates rules that allow to recover several known forms of time consistency, and to study some new forms of time consistency
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