Reduction of Value-at-Risk Bounds via Independence and Variance Information

Puccetti, Giovanni; Rüschendorf, Ludger; Small, Daniel; Vanduffel, Steven

doi:10.2139/ssrn.2584860

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Reduction of Value-at-Risk Bounds via Independence and Variance Information

Forthcoming in Scandinavian Actuarial Journal

18 Pages Posted: 27 Mar 2015 Last revised: 11 Nov 2015

See all articles by Giovanni Puccetti

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM)

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: September 30, 2015

Abstract

We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and independence among (some) subgroups of the marginal components is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. When the variance of the joint portfolio loss is small enough, further improvements can be obtained.

Keywords: Value-at-Risk, Dependence Uncertainty, Model Risk, Expected Shortfall

JEL Classification: B30, E15

Suggested Citation: Suggested Citation

Puccetti, Giovanni and Rüschendorf, Ludger and Small, Daniel and Vanduffel, Steven, Reduction of Value-at-Risk Bounds via Independence and Variance Information (September 30, 2015). Forthcoming in Scandinavian Actuarial Journal, Available at SSRN: https://ssrn.com/abstract=2584860 or http://dx.doi.org/10.2139/ssrn.2584860