Range Value-at-Risk Bounds for Unimodal Distributions under Partial Information

39 Pages Posted: 30 Jun 2019 Last revised: 24 Jun 2020

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Rodrigue Kazzi

Vrije Universiteit Brussel (VUB)

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: January 17, 2020

Abstract

In this paper, we derive upper and lower bounds on the Range Value-at-Risk of the portfolio loss when we only know its mean and variance, and its feature of unimodality. In a first step, we use some classic results on stochastic ordering to reduce this optimization problem to a parametric one, which in a second step can be solved using standard methods. The novel approach we propose makes it possible to obtain analytical results for all probability levels and is moreover amendable to other situations of interest. Specifically, we apply our method to obtain risk bounds in the case of a portfolio loss that is non-negative (as is often the case in practice) and whose variance is possibly infinite. Numerical illustrations show that in various cases of interest we obtain bounds that are of practical importance.

Keywords: Model risk, Value-at-Risk, Tail Value-at-Risk, Range Value-at-Risk, Convex ordering, Unimodal distributions, Risk bounds

JEL Classification: C02, C52, C61, D81

Suggested Citation

Bernard, Carole and Kazzi, Rodrigue and Vanduffel, Steven, Range Value-at-Risk Bounds for Unimodal Distributions under Partial Information (January 17, 2020). Insurance: Mathematics and Economics, Vol. 94, p. 9-24, September 2020, Available at SSRN: https://ssrn.com/abstract=3412158 or http://dx.doi.org/10.2139/ssrn.3412158

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Rodrigue Kazzi (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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