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Bivariate compound renewal sums with discounted claims

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Abstract

Recursive moments, joint moments, moments generating functions, distribution functions, stop-loss premiums and risk measures have been found for the univariate compound renewal sums with discounted claims, for a constant force of real interest. More recently, moments and joint moments have also been found when the force of interest is stochastic. In this paper, we extend some of the preceding results to the bivariate compound renewal sums with discounted claims by first presenting a lemma that gives the conditional joint distribution of the occurrence times of the claims given the number of claims of each type up to time t, result that will be used to get the second moment, the first joint moment and other quantities related to our bivariate risk process.

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Authors and Affiliations

  1. École d’actuariat, Université Laval, 1045 Avenue de la Médecine, Pavillon Alexandre-Vachon, Local 1620, Quebec, G1V 0A6, Canada

    Ghislain Léveillé

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  1. Ghislain Léveillé
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Correspondence to Ghislain Léveillé.

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Léveillé, G. Bivariate compound renewal sums with discounted claims. Eur. Actuar. J. 2, 273–288 (2012). https://doi.org/10.1007/s13385-012-0054-4

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  • DOI: https://doi.org/10.1007/s13385-012-0054-4

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