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Recursions for the Individual Risk Model

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Abstract

In the actuarial literature, several exact and approximative recursive methods have been proposed for calculating the distribution of a sum of mutually independent compound Bernoulli distributed random variables. In this paper, we give an overview of these methods. We compare their performance with the straightforward convolution technique by counting the number of dot operations involved in each method. It turns out that in many practicle situations, the recursive methods outperform the convolution method.

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Authors and Affiliations

  1. Katholieke Universiteit Leuven, Belgium and Universiteit van Amsterdam, The Netherlands

    Jan Dhaene*

  2. University of Barcelona, Barcelona, Spain

    Carmen Ribas

  3. Ovidius University of Constanta, Constanta, Romania

    Raluca Vernic***

Authors
  1. Jan Dhaene*
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  2. Carmen Ribas
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  3. Raluca Vernic***
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Corresponding author

Correspondence to Jan Dhaene*.

Additional information

*Support by the Onderzoeksfonds K.U.Leuven (GOA/02: Actuariële, financiële en statistische aspecten van afhankelijkheden in verzekerings- en financiële portefeuilles).

***Support by the Dutch Organization for Scientific Research (No. NWO 048.031.2003.001).

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Dhaene*, J., Ribas, C. & Vernic***, R. Recursions for the Individual Risk Model. Acta Math. Appl. Sin, Engl. Ser. 22, 543–564 (2006). https://doi.org/10.1007/s10255-006-0329-0

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  • DOI: https://doi.org/10.1007/s10255-006-0329-0

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