Resumen de Modelling dependent risks with heavy-tail marginals
José María Sarabia Alegría, Montserrat Guillén Estany, Faustino Prieto Mendoza, Vanesa Jordá Gil
In this paper we present a general class of dependent risks, where the individual risks are represented according to second kind beta distributions. The second kind beta distribution, characterized by three parameters, is considered a suitable model in risk management because it has heavy tails and many of the risk measures are available in a closed form. First, we define a vector of dependent risk, where the marginals are second kind beta distributions and the dependence arises in the form of a common factor. One of the advantages of the multivariate model is that many of its features (risk measures, risk aggregation, etc.) can be easily obtained by simulation. We study the basic properties of the new dependent risks model, including the joint density function, marginal and conditional distributions. We also discuss the aggregated random variable for which we obtain analytic formulas for the probability density function. After describing the estimation of the model by maximum likelihood, we provide initial estimates for the parameters based on the method of moments. We illustrate the performance of the model with an application with a data set containing information about losses from individual insurance policies.
