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

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

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.

Suggested Citation

  • Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
  • Handle: RePEc:eee:insuma:v:106:y:2022:i:c:p:364-389
    DOI: 10.1016/j.insmatheco.2022.07.001
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    More about this item

    Keywords

    Matrix-exponential distribution; Multivariate affine mixtures; Risk measures; Capital allocation; Multiplicative background risk models;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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