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 t...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 straight- forward 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.展开更多
In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 （Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Jo...In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 （Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Journal 8） to model insurance aggregate claims in the case when different types of claims simulta- neously affect an insurance portfolio. We obtain an exact recursive formula for the probability function of the multivariate compound distribution corresponding to this model under the assumption that the conditional multivariate counting distribution （conditioned by the total number of claims） is multinomial. Our formula extends the corresponding one from Jin and Ren.展开更多
基金Support by the Onderzoeksfonds K.U.Leuven(GOA/02:Actuarile,financile en statistische aspecten van afhankelijkheden in vcrzekerings-en financile portefeuilles)Support by the Dutch Organization for Scientific Research(No.NWO 048.031.2003.001)
文摘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 straight- forward 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.
文摘In this paper, we extend to a multivariate setting the bivariate model A introduced by Jin and Ren in 2014 （Recursions and fast Fourier transforms for a new bivariate aggregate claims model, Scandinavian Actuarial Journal 8） to model insurance aggregate claims in the case when different types of claims simulta- neously affect an insurance portfolio. We obtain an exact recursive formula for the probability function of the multivariate compound distribution corresponding to this model under the assumption that the conditional multivariate counting distribution （conditioned by the total number of claims） is multinomial. Our formula extends the corresponding one from Jin and Ren.
