QA516 : Risk aggregation in multivariate dependent Pareto distributions
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2018
Authors:
Seyede Mona MirHojati [Author], Ahmad Nezakati Rezazadeh[Supervisor], Sayyed Mojtaba Mirlohi[Supervisor]
Abstarct: In this dissertation we obtain closed exxpressions 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 Value at Risk and several other risk measures. Then, we consider a collective risk model baxsed on dependence, where several general properties are studied. We study in detail some relevant collective models with Poisson, negative binomial and geometric 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.With reviews on data baxsed on one-year insurance policies annually (2004-2005) And the data of Iran's insurance company was carried out in 93، we conclude that our collective dependent models outperform other collective models considered in the actuarial literature in terms of AIC statistics.
Keywords:
#Dependent risk Individual risk model Collective risk model Classical Pareto distribution Hypergeometric function Link
Keeping place: Central Library of Shahrood University
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