Risk aggregation in multivariate dependent Pareto distributions

José María Sarabia, Emilio Gómez-Déniz, Faustino Prieto and Vanesa Jordá

Insurance: Mathematics and Economics, 2016, vol. 71, issue C, 154-163

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.

Keywords: Dependent risks; Individual risk model; Collective risk model; Classical Pareto distribution; Hypergeometric functions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:71:y:2016:i:c:p:154-163

DOI: 10.1016/j.insmatheco.2016.07.009

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