Upper bounds for strictly concave distortion risk measures on moment spaces
L. Rüschendorf and
Insurance: Mathematics and Economics, 2018, vol. 82, issue C, 141-151
The study of worst-case scenarios for risk measures (e.g., Value-at-Risk) when the underlying risk (or portfolio of risks) is not completely specified is a central topic in the literature on robust risk measurement. In this paper, we tackle the open problem of deriving upper bounds for strictly concave distortion risk measures on moment spaces. Building on early results of Rustagi (1957, 1976), we show that in general this problem can be reduced to a parametric optimization problem. We completely specify the sharp upper bound (and corresponding maximizing distribution function) when the first moment and any other higher moment are fixed. Specifically, in the case of a fixed mean and variance, we generalize the Cantelli bound for (Tail) Value-at-Risk in that we express the sharp upper bound for a strictly concave distorted expectation as a weighted sum of the mean and standard deviation.
Keywords: Value-at-Risk (vaR); Coherent risk measure; Model uncertainty; Cantelli bound; Distortion function (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
Full text for ScienceDirect subscribers only
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:82:y:2018:i:c:p:141-151
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 Dana Niculescu ().