  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.
