Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions
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Identificadores
URI: http://hdl.handle.net/10902/15072DOI: 10.1017/asb.2018.13
ISSN: 0515-0361
ISSN: 1783-1350
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2018Derechos
© Cambridge University Press
Publicado en
ASTIN bulletin Volume 48, Issue 3 September 2018 , pp. 1079-1107
Editorial
Cambridge University Press
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Palabras clave
Aggregation
Dependent random variables
Laplace transform
Collective risk model
Partial Bell polynomials
Resumen/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, modeled 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.
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