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Risks 2018, 6(3), 87; https://doi.org/10.3390/risks6030087

On the Evaluation of the Distribution of a General Multivariate Collective Model: Recursions versus Fast Fourier Transform

1
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, 900527 Constanta, Romania
2
Institute for Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
Received: 26 July 2018 / Revised: 22 August 2018 / Accepted: 23 August 2018 / Published: 26 August 2018
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Abstract

With the purpose of introducing dependence between different types of claims, multivariate collective models have recently gained a lot of attention. However, when it comes to the evaluation of the corresponding compound distribution, the problems increase with the dimensionality of the model. In this paper, we consider a multivariate collective model that generalizes a model already studied from the point of view of recursive and FFT evaluation of its distribution, and we extend the same study to the general model. With the intention to see which method works better for this general model, we compare the recursive method with the FFT technique, and emphasize the advantages and drawbacks of each one, based on numerical examples. View Full-Text
Keywords: multivariate collective model; multivariate compound distribution; recursions; Fast Fourier Transform multivariate collective model; multivariate compound distribution; recursions; Fast Fourier Transform
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Vernic, R. On the Evaluation of the Distribution of a General Multivariate Collective Model: Recursions versus Fast Fourier Transform. Risks 2018, 6, 87.

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