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
Annals of Operations Research – Springer Journals
Published: May 31, 2018
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