@article{10902/15786,
year = {2018},
month = {6},
url = {http://hdl.handle.net/10902/15786},
abstract = {We apply distortion functions to bivariate survival functions for nonnegative random variables. This leads to a natural extension of univariate distortion risk measures to the multivariate setting. For Gini?s principle, the proportional hazard transform distortion and the dual power transform distortion, certain families of multivariate distributions lead to a straightforward risk measure.We showthat an exact analytical expression can be obtained in some cases. We consider the independence case, the bivariate Pareto distribution and the bivariate exponential distribution.An illustration of the estimation procedure and the interpretation is also included. In the case study, we consider two loss events with a single risk value and monitor the two events together over four different periods. We conclude that the dual power transform gives more weight to  the observations of extreme losses, but that the distortion parameter can modulate this influence in all cases. In our example, multivariate risk clearly diminishes over time.},
organization = {The authors acknowledge the support received from the Spanish Ministry of Science/
FEDER grants ECO2016-76203-C2-1-P and ECO2016-76203-C2-2-P, and
J. M. Sarabia and F. Prieto acknowledge the support received from the Santander
Financial Institute (SANFI) of the Fundación UCEIF through the University of
Cantabria, funded by sponsorship from Banco Santander.},
publisher = {Infopro Digital Limited},
publisher = {Journal of Operational Risk, 2018, vol. 13, num. 2, p. 35-57.},
title = {Distortion risk measures for nonnegative multivariate risks.},
author = {Guillén, Montserrat and Sarabia Alegría, José María and Belles Sampera, Jaume and Prieto Mendoza, Faustino},
}