  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.
