Multivariate matrix-exponential affine mixtures and their applications in risk theory
Abstract
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.
Cite
@article{arxiv.2201.11122,
title = {Multivariate matrix-exponential affine mixtures and their applications in risk theory},
author = {Eric C. K. Cheung and Oscar Peralta and Jae-Kyung Woo},
journal= {arXiv preprint arXiv:2201.11122},
year = {2022}
}