MA thesis defence in Mathematics

Speaker:  Ms. Lu Cao (MA)

Abstract: The dependence between random variables has to be accounted for modeling risk measures in a multivariate setting. In this thesis, we propose a bivariate extension of the robust risk measure Range Value-at-Risk (RVaR) based on bivariate lower and upper orthant Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) introduced by Cossette et al. (2013, 2015). They are shown to possess properties similar to bivariate TVaR, such as translation invariance, positive homogeneity and monotonicity. Examples with different copulas are provided. Also, we present the consistent empirical estimators of bivariate RVaR along with the simulation. The robustness of estimators of bivariate VaR, TVaR and RVaR are discussed with the help of their sensitivity functions. We conclude that the bivariate VaR and RVaR are robuststatistics.