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arXiv · 2201.11122

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

Eric C. K. Cheung·Oscar Peralta·Jae-Kyung Woo
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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.

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Eric C. K. Cheung, Oscar Peralta, Jae-Kyung Woo. 2021-12-17. Multivariate matrix-exponential affine mixtures and their applications in risk theory. https://arxiv.org/abs/2201.11122

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