Economics at your fingertips  

Model-free bounds on Value-at-Risk using extreme value information and statistical distances

Thibaut Lux and Antonis Papapantoleon

Insurance: Mathematics and Economics, 2019, vol. 86, issue C, 73-83

Abstract: We derive bounds on the distribution function, therefore also on the Value-at-Risk, of φ(X) where φ is an aggregation function and X=(X1,…,Xd) is a random vector with known marginal distributions and partially known dependence structure. More specifically, we analyze three types of available information on the dependence structure: First, we consider the case where extreme value information, such as the distributions of partial minima and maxima of X, is available. In order to include this information in the computation of Value-at-Risk bounds, we utilize a reduction principle that relates this problem to an optimization problem over a standard Fréchet class, which can then be solved by means of the rearrangement algorithm or using analytical results. Second, we assume that the copula of X is known on a subset of its domain, and finally we consider the case where the copula of X lies in the vicinity of a reference copula as measured by a statistical distance. In order to derive Value-at-Risk bounds in the latter situations, we first improve the Fréchet–Hoeffding bounds on copulas so as to include this additional information on the dependence structure. Then, we translate the improved Fréchet–Hoeffding bounds to bounds on the Value-at-Risk using the so-called improved standard bounds. In numerical examples we illustrate that the additional information typically leads to a significant improvement of the bounds compared to the marginals-only case.

Keywords: Value-at-Risk bounds; Dependence uncertainty; Copulas; Improved Fréchet–Hoeffding bounds; Distribution of maxima and minima; Reduction principle; Distance to reference copula; Rearrangement algorithm (search for similar items in EconPapers)
JEL-codes: G32 C52 C60 (search for similar items in EconPapers)
Date: 2019
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

Related works:
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:

DOI: 10.1016/j.insmatheco.2019.01.007

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 Haili He ().

Page updated 2020-05-02
Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:73-83