Law-invariant return and star-shaped risk measures

Roger Laeven, Emanuela Rosazza Gianin and Marco Zullino

Insurance: Mathematics and Economics, 2024, vol. 117, issue C, 140-153

Abstract: This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts.

Keywords: Return risk measures; Star-shapedness; Law-invariance; SSD- and CSD-consistency; Value-at-risk; Expected shortfall (search for similar items in EconPapers)
JEL-codes: D81 G10 G20 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: Law-Invariant Return and Star-Shaped Risk Measures (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:117:y:2024:i:c:p:140-153

DOI: 10.1016/j.insmatheco.2024.04.006

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