Multivariate double truncated expectation and covariance risk measures for elliptical distributions

The main objective of this work is to calculate the multivariate double truncated expectation (MDTE) and covariance (MDTCov) for elliptical distributions. We also consider double truncated expectation (DTE) and variance (DTV) for univariate elliptical distributions. The exact expressions of MDTE and MDTCov are derived for some special cases of the family, such as normal, student-$t$, logistic, Laplace and Pearson type VII distributions. As numerical illustration, the DTE, DTV, MDTE and MDTCov for normal distribution are computed in details. Finally, we discuss MDTE and MDTCov of three industry segments' (Banks, Insurance, Financial and Credit Service) stock return in London stock exchange.