  In this paper we obtain closed expressions for the probability distribution
function, when we consider aggregated risks with multivariate dependent Pareto
distributions. We work with the dependent multivariate Pareto type II proposed
by Arnold (1983, 2015), which is widely used in insurance and risk analysis. We
begin with the individual risk model, where we obtain the probability density
function (PDF), which corresponds to a second kind beta distribution. We obtain
several risk measures including the VaR, TVaR and other tail measures. Then, we
consider collective risk model based on dependence, where several general
properties are studied. We study in detail some relevant collective models with
Poisson, negative binomial and logarithmic distributions as primary
distributions. In the collective Pareto-Poisson model, the PDF is a function of
the Kummer confluent hypergeometric function, and in the Pareto-negative
binomial is a function of the Gauss hypergeometric function. Using the data set
based on one-year vehicle insurance policies taken out in 2004-2005 (Jong and
Heller, 2008), we conclude that our collective dependent models outperform the
classical collective models Poisson-exponential and geometric-exponential in
terms of the AIC and CAIC statistics.
