A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

TL;DR

This paper provides a comprehensive survey of the time consistency of dynamic risk and performance measures in discrete time, emphasizing the LM-measure perspective and update rules as key tools.

Contribution

It offers a unified framework for understanding time consistency in dynamic measures using LM-measures and update rules, consolidating existing knowledge.

Findings

Highlights the importance of LM-measures and update rules in analyzing time consistency.

Provides a systematic overview of existing results in the field.

Identifies key properties and conditions for time consistency in discrete-time measures.

Abstract

In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the LM-measure and the notion of the update rule that, we believe, are the key tools for studying time consistency in a unified framework.