A concept of copula robustness and its applications in quantitative risk management

by Henryk Zähle1
1 Department of Mathematics, Saarland University, 66123 Saarbrücken, Germany
(email: zaehle@math.uni-sb.de)


In financial and actuarial applications, marginal risks and their dependence structure are often modelled separately. While it is sometimes reasonable to assume that the marginal distributions are `known', it is usually quite involved to obtain information on the copula (dependence structure). Therefore copula models used in practice are quite often only rough guesses. For many purposes it is thus relevant to know whether certain characteristics derived from d-variate risks are robust with respect to (at least small) deviations in the copula. In this article, a general concept of copula robustness is introduced and criteria for copula robustness are presented. These criteria are illustrated by means of several examples from quantitative risk management. The concept of aggregation robustness introduced by Embrechts et al. (Aggregation-robustness and model uncertainty of regulatory risk measures; Finance and Stochastics, 19, 763--790, (2015)) can be embedded in the framework of copula robustness.

Key words:

Copula, Fréchet class, Lp-weak topology, Risk measure, Portfolio optimisation
JEL Classification:  C02, C60, G11
Mathematics Subject Classification (2020):  62H05, 60B10, 90C17, 91G70