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On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution

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  • Vernic, Raluca

Abstract

In this paper, we consider Sarmanov’s multivariate discrete distribution as counting distribution in two multivariate compound models: the first model assumes different types of independent claim sizes (corresponding to, e.g., different types of insurance policies), while in the second model, we introduce some dependency between the claims (motivated by the events that can simultaneously affect several types of policies). Since Sarmanov’s distribution can join different types of marginals, we also assume that these marginals belong to Panjer’s class of distributions and discuss the evaluation of the resulting compound distribution based on recursions. Alternatively, the evaluation of the same distribution using the Fast Fourier Transform method is also presented, with the purpose to significantly reduce the computing time, especially in the dependency case. Both methods are numerically illustrated and compared from the point of view of speed and accuracy.

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  • 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.
    • Handle: RePEc:eee:insuma:v:79:y:2018:i:c:p:184-193
    DOI: 10.1016/j.insmatheco.2018.01.006
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    References listed on IDEAS

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    Cited by:

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    3. Syuhada, Khreshna & Tjahjono, Venansius & Hakim, Arief, 2024. "Compound Poisson–Lindley process with Sarmanov dependence structure and its application for premium-based spectral risk forecasting," Applied Mathematics and Computation, Elsevier, vol. 467(C).
    4. Raluca Vernic, 2018. "On the Evaluation of the Distribution of a General Multivariate Collective Model: Recursions versus Fast Fourier Transform," Risks, MDPI, vol. 6(3), pages 1-14, August.

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