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On some multivariate Sarmanov mixed Erlang reinsurance risks: Aggregation and capital allocation

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  • Ratovomirija, Gildas
  • Tamraz, Maissa
  • Vernic, Raluca

Abstract

Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov’s multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a different kernel function for Sarmanov’s distribution, not previously studied in this context. The risk aggregation and capital allocation formulas are derived and numerically illustrated in the general framework of stop-loss reinsurance, and then in the particular case with no stop-loss reinsurance. A discussion of the dependency structure of the considered distribution, based on Pearson’s correlation coefficient, is also presented for different kernel functions and illustrated in the bivariate case.

Suggested Citation

  • Ratovomirija, Gildas & Tamraz, Maissa & Vernic, Raluca, 2017. "On some multivariate Sarmanov mixed Erlang reinsurance risks: Aggregation and capital allocation," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 197-209.
    • Handle: RePEc:eee:insuma:v:74:y:2017:i:c:p:197-209
    DOI: 10.1016/j.insmatheco.2017.03.009
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    References listed on IDEAS

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    Cited by:

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    6. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    7. Khouzeima Moutanabbir & Hassan Abdelrahman, 2022. "Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1093-1118, June.
    8. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
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    10. 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.

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