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

Tomasz R. Bielecki; Igor Cialenco; Marcin Pitera

doi:10.1186/s41546-017-0012-9

Article Contents

2017, Volume 2: 3. Doi: 10.1186/s41546-017-0012-9

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

1 Department of Applied Mathematics, Illinois Institute of Technology, 10 W 32 nd Str, Building E1, Room 208, Chicago, IL 60616, USA;
2 Institute of Mathematics, Jagiellonian University, Cracow, Poland

Tomasz R. Bielecki, tbielecki@iit.edu ; Igor Cialenco, cialenco@iit.edu ; Marcin Pitera, marcin.pitera@im.uj.edu.pl

Received: March 29, 2016

Revised: December 17, 2016

Published: September 2020

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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 LMmeasure and the notion of the update rule that, we believe, are the key tools for studying time consistency in a unified framework.

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Mathematics Subject Classification: 91B30;62P05;97M30;91B06.

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