Multivariate matrix-exponential affine mixtures and their applications in risk theory

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