@article{10902/15072,
year = {2018},
url = {http://hdl.handle.net/10902/15072},
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.},
organization = {The authors thanks to the Ministerio de Econom´ıa y Competitividad (projects
ECO2016-76203-C2-1-P, JMS, FP and VJ ECO2013-47092 EGD) for partial
support of this work. In addition, this work is part of the Research Project
APIE 1/2015-17 (JMS, FP, VJ): “New methods for the empirical analysis of
financial markets” of the Santander Financial Institute (SANFI) of UCEIF
Foundation resolved by the University of Cantabria and funded with sponsorship from Banco Santander.},
publisher = {Cambridge University Press},
publisher = {ASTIN bulletin Volume 48, Issue 3 September 2018 , pp. 1079-1107},
title = {Aggregation of Dependent Risks in Mixtures of Exponential Distributions and Extensions},
author = {Sarabia Alegría, José María and Gómez Déniz, Emilio and Prieto Mendoza, Faustino and Jordá, Vanesa},
}