Reducing Model Risk via Positive and Negative Dependence Assumptions

12 Pages Posted: 5 Sep 2014 Last revised: 12 May 2015

See all articles by Valeria Bignozzi

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Giovanni Puccetti

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

Ludger Rüschendorf

University of Freiburg

Date Written: 2014

Abstract

We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence uncertainty spreads compared to the case where only marginals information is known. In more detail, we show that in our model the assumption of a positive dependence structure improves the best-possible lower estimate of a risk measure, while leaving unchanged its worst-possible upper risk bounds. In a similar way, we derive for convex risk measures that the assumption of a negative dependence structure leads to improved upper bounds for the risk while it does not help to increase the lower risk bounds in an essential way. As a result we find that additional assumptions on the dependence structure may result in essentially improved risk bounds.

Suggested Citation

Bignozzi, Valeria and Puccetti, Giovanni and Rüschendorf, Ludger, Reducing Model Risk via Positive and Negative Dependence Assumptions (2014). Insurance Math. Econ. 61(1), 17-26, 2015. Available at SSRN: https://ssrn.com/abstract=2490984 or http://dx.doi.org/10.2139/ssrn.2490984

Valeria Bignozzi (Contact Author)

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Via Bicocca degli Arcimboldi, 8
Milano, 20126
Italy

Giovanni Puccetti

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

Via Conservatorio, 7
Milan, 20122
Italy

Ludger Rüschendorf

University of Freiburg ( email )

Fahnenbergplatz
Freiburg, D-79085
Germany

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