Multivariate Robust Vector-Valued Range Value-at-Risk

In a multivariate setting, the dependence between random variables has to be accounted for modeling purposes. Various of multivariate risk measures have been developed, including bivariate lower and upper orthant Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR). The robustness of their estimators has to be discussed with the help of sensitivity functions, since risk measures are estimated from data. In this thesis, several univariate risk measures and their multivariate extensions are presented. In particular, we are interested in developing the bivariate version of a robust risk measure called Range Value-at-Risk (RVaR). Examples with different copulas, such as the Archimedean copula, are provided. Also, properties such as translation invariance, positive homogeneity and monotonicity are examined. Consistent empirical estimators are also presented along with the simulation. Moreover, the sensitivity functions of the bivariate VaR, TVaR and RVaR are obtained, which confirms the robustness of bivariate VaR and RVaR as expected