Inter-order relations between equivalence for Lp-quantiles of the Student's t distribution

Valeria Bignozzi, Luca Merlo and Lea Petrella

Insurance: Mathematics and Economics, 2024, vol. 116, issue C, 44-50

Abstract: In the statistical and actuarial literature, Lp-quantiles, p∈[1,+∞), represent an important class of risk measures defined through an asymmetric p-power loss function that generalize the classical (L1-)quantiles. By exploiting inter-order relations between partial moments, we show that for a Student's t distribution with ν∈[1,+∞) degrees of freedom the Lν−j-quantile and the Lj+1-quantile always coincide for any j∈[0,ν−1]. For instance, for a Student's t distribution with 4 degrees of freedom, the L4-quantile and L1-quantile are equal and the same holds for the L3-quantile and L2-quantile; for this distribution, closed form expressions for the Lp-quantile, p=1,2,3,4 are provided. Explicit formulas for the central moments are also established. The usefulness of exact formulas is illustrated on real-world financial data.

Keywords: Expectiles; Generalized quantiles; Partial moments; Quantiles; Risk measures (search for similar items in EconPapers)
JEL-codes: C1 C21 G22 G32 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:116:y:2024:i:c:p:44-50

DOI: 10.1016/j.insmatheco.2024.02.001

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