  In this paper, we, for the first time, establish two comparison theorems for
multi-dimensional backward stochastic differential equations with jumps. Our
approach is novel and completely different from the existing results for
one-dimensional case. Using these and other delicate tools, we then construct
solutions to coupled two-dimensional stochastic Riccati equation with jumps in
both standard and singular cases. In the end, these results are applied to
solve a cone-constrained stochastic linear-quadratic and a mean-variance
portfolio selection problem with jumps. Different from no jump problems, the
optimal (relative) state processes may change their signs, which is of course
due to the presence of jumps.
