Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks

Tiantian Mao, Gilles Stupfler and Fan Yang

Insurance: Mathematics and Economics, 2023, vol. 111, issue C, 173-192

Abstract: We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative prospect theory. This risk measure can be flexibly designed to capture the decision maker's behavior toward risks and wealth when measuring risk. In this paper, we derive the first- and second-order asymptotic expansions for the generalized shortfall risk measure. Our asymptotic results can be viewed as unifying theory for, among others, distortion risk measures and utility-based shortfall risk measures. They also provide a blueprint for the estimation of these measures at extreme levels, and we illustrate this principle by constructing and studying a quantile-based estimator in a special case. The accuracy of the asymptotic expansions and of the estimator is assessed on several numerical examples.

Keywords: Generalized shortfall risk measure; Asymptotic expansions; Heavy tails; Estimation; Extreme value statistics (search for similar items in EconPapers)
JEL-codes: C02 C13 G10 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668723000392
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Asymptotic Properties of Generalized Shortfall Risk Measures for Heavy-tailed Risks (2024)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:111:y:2023:i:c:p:173-192

DOI: 10.1016/j.insmatheco.2023.05.001

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().