How to Get Bounds for Distribution Convolutions? A Simulation Study and an Application to Risk Management

14 Pages Posted: 26 Nov 2007 Last revised: 3 Apr 2009

See all articles by Valdo Durrleman

Valdo Durrleman

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS

Ashkan Nikeghbali

affiliation not provided to SSRN

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: September 10, 2000

Abstract

In this paper, we consider the problem of bounds for distribution convolutions and we present some applications to risk management. We show that the upper Frechet bound is not always the more risky dependence structure. It is in contradiction with the belief in finance that maximal risk corresponds to the case where the random variables are comonotonic.

Keywords: Triangle functions, dependency bounds, infimal, supremal and sigma-convolutions, Makarov inequalities, Value-at-Risk, square root rule, Dall'aglio problem, Kantorovich distance

JEL Classification: G00

Suggested Citation

Durrleman, Valdo and Nikeghbali, Ashkan and Roncalli, Thierry, How to Get Bounds for Distribution Convolutions? A Simulation Study and an Application to Risk Management (September 10, 2000). Available at SSRN: https://ssrn.com/abstract=1032554 or http://dx.doi.org/10.2139/ssrn.1032554

Valdo Durrleman

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS ( email )

Palaiseau, 91128
France

Ashkan Nikeghbali

affiliation not provided to SSRN ( email )

No Address Available

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

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