Law-Invariant Return and Star-Shaped Risk Measures

Roger Laeven, Emanuela Rosazza Gianin and Marco Zullino

Papers from arXiv.org

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.

Date: 2023-10
New Economics Papers: this item is included in nep-rmg
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Citations: View citations in EconPapers (2)

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Journal Article: Law-invariant return and star-shaped risk measures (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2310.19552

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