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http://hdl.handle.net/10553/42119
Título: | Risk aggregation in multivariate dependent Pareto distributions | Autores/as: | Sarabia, José María Gómez-Déniz, Emilio Prieto, Faustino Jordá, Vanesa |
Clasificación UNESCO: | 1206 Análisis numérico 1209 Estadística |
Palabras clave: | Classical Pareto distribution Collective risk model Dependent risks Hypergeometric functions Individual risk model |
Fecha de publicación: | 2016 | Publicación seriada: | Insurance: Mathematics and Economics | Resumen: | 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. | URI: | http://hdl.handle.net/10553/42119 | ISSN: | 0167-6687 | DOI: | 10.1016/j.insmatheco.2016.07.009 | Fuente: | Insurance: Mathematics and Economics[ISSN 0167-6687],v. 71, p. 154-163 |
Colección: | Artículos |
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