On the link between monetary and star-shaped risk measures

Marlon Ruoso Moresco and Marcelo Righi ()

Statistics & Probability Letters, 2022, vol. 184, issue C

Abstract: Recently, Castagnoli et al. (2021) introduced the class of star-shaped risk measures as a generalization of convex and coherent ones, proving that there is a representation as the pointwise minimum of some family composed by convex risk measures. Concomitantly, Jia et al. (2020) prove a similar representation result for monetary risk measures, which are more general than star-shaped ones. Then, there is a question on how both classes are connected. In this letter, we provide an answer by casting light on the importance of the acceptability of 0, which is linked to the property of normalization. We then show that under mild conditions, a monetary risk measure is only a translation away from star-shapedness.

Keywords: Risk measures; Star-shapedness; Acceptance sets; Representations; Convex risk measures (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (8)

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DOI: 10.1016/j.spl.2021.109345

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