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Title: Risk aggregation in multivariate dependent Pareto distributions
Authors: Sarabia, José María
Gómez-Déniz, Emilio 
Prieto, Faustino
Jordá, Vanesa
UNESCO Clasification: 1206 Análisis numérico
1209 Estadística
Keywords: Classical Pareto distribution
Collective risk model
Dependent risks
Hypergeometric functions
Individual risk model
Issue Date: 2016
Journal: Insurance: Mathematics and Economics 
Abstract: In this paper we obtain closed expressions for the probability distribution function of 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 an individual risk model, where the probability density function corresponds to a second kind beta distribution, obtaining the VaR, TVaR and several other tail risk measures. Then, we consider a 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 probability density function is a function of the Kummer confluent hypergeometric function, and the density of the Pareto–negative binomial is a function of the Gauss hypergeometric function. Using data based on one-year vehicle insurance policies taken out in 2004–2005 (Jong and Heller, 2008) we conclude that our collective dependent models outperform other collective models considered in the actuarial literature in terms of AIC and CAIC statistics.
ISSN: 0167-6687
DOI: 10.1016/j.insmatheco.2016.07.009
Source: Insurance: Mathematics and Economics[ISSN 0167-6687],v. 71, p. 154-163
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