  In this paper, a class of multivariate matrix-exponential affine mixtures
with matrix-exponential marginals is proposed. The class is shown to possess
various attractive properties such as closure under size-biased Esscher
transform, order statistics, residual lifetime and higher order equilibrium
distributions. This allows for explicit calculations of various actuarial
quantities of interest. The results are applied in a wide range of actuarial
problems including multivariate risk measures, aggregate loss, large claims
reinsurance, weighted premium calculations and risk capital allocation.
Furthermore, a multiplicative background risk model with dependent risks is
considered and its capital allocation rules are provided as well. We finalize
by discussing a calibration scheme based on complete data and potential avenues
of research.
