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

Eric C.K. Cheung, Oscar Peralta and Jae-Kyung Woo

Insurance: Mathematics and Economics, 2022, vol. 106, issue C, 364-389

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.

Keywords: Matrix-exponential distribution; Multivariate affine mixtures; Risk measures; Capital allocation; Multiplicative background risk models (search for similar items in EconPapers)
JEL-codes: C02 C46 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:106:y:2022:i:c:p:364-389

DOI: 10.1016/j.insmatheco.2022.07.001

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