Estimating asymptotic dependence functionals in multivariate regularly varying models (Q1943759)

The paper is concerned with the portfolio risk index \(\gamma_\xi\) and its estimation for real random vectors. Based on multivariation regular variation this index measures the extreme risk of the weighted portfolio \(\sum\limits_{i=1}^{d} \xi_i X_i\). The paper extends some results of the present author and \textit{L. Rüschendorf} [Finance Stoch. 14, No. 4, 593--623 (2010; Zbl 1226.91069)] for the case of positive losses to the general loss case and obtains consistency and asymptotic normality results under modified regularity conditions.