Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/42204
Title: Aggregation of dependent risks inmixtures of exponential distributions and extensions
Authors: Sarabia, José María
Gómez-Déniz, Emilio 
Prieto, Faustino
Jordá, Vanesa
UNESCO Clasification: 53 Ciencias económicas
Keywords: Aggregation
Dependent random variables
Laplace transform
Collective risk model
Partial Bell polynomials
Issue Date: 2018
Publisher: 0515-0361
Journal: ASTIN Bulletin 
Abstract: The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modelled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al., 2016), gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research.
URI: http://hdl.handle.net/10553/42204
ISSN: 0515-0361
DOI: 10.1017/asb.2018.13
Source: ASTIN Bulletin[ISSN 0515-0361],v. 48, p. 1079-1107
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