A composition between risk and deviation measures

A composition between risk and deviation measures Ann Oper Res https://doi.org/10.1007/s10479-018-2913-0 S.I.: APPLICATION OF O. R. TO FINANCIAL MARKETS Marcelo Brutti Righi © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed. We also provide examples of known and new risk measures constructed under this framework in order to highlight the importance of our approach, especially the role of the Limitedness axiom. Keywords Coherent risk measures · Generalized deviation measures · Convex risk measures · Co-monotone coherent risk measures · Limitedness 1 Introduction The intuition of risk is based on two main concepts: the possibility of a negative outcome, i.e. a loss; and the variability in terms of an expected result, i.e. a deviation. Since the time when the modern theory of finance was accepted, the role of risk measurement has attracted attention. Initially, it was predominantly used http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

A composition between risk and deviation measures

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-018-2913-0
Publisher site
See Article on Publisher Site

Abstract

Ann Oper Res https://doi.org/10.1007/s10479-018-2913-0 S.I.: APPLICATION OF O. R. TO FINANCIAL MARKETS Marcelo Brutti Righi © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed. We also provide examples of known and new risk measures constructed under this framework in order to highlight the importance of our approach, especially the role of the Limitedness axiom. Keywords Coherent risk measures · Generalized deviation measures · Convex risk measures · Co-monotone coherent risk measures · Limitedness 1 Introduction The intuition of risk is based on two main concepts: the possibility of a negative outcome, i.e. a loss; and the variability in terms of an expected result, i.e. a deviation. Since the time when the modern theory of finance was accepted, the role of risk measurement has attracted attention. Initially, it was predominantly used

Journal

Annals of Operations ResearchSpringer Journals

Published: May 31, 2018

References

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