Desarrollo de modelo Bayesiano jerárquico de mezcla con número de componentes aleatorio para cuantificar el riesgo de suscripción en seguros de no vida

Abstract

The purpose of this project is developmenting a fully Bayesian hierarchical mixture model with a random number of components, in order to quantify the risk of subscription in non-life insurance. Subscription risk from the point of view of pricing is associated with an insurance company's probability of insolvency. This probability depends on a ruin stochastic process who is in function of the initial capital of the company, the total premiums received and the aggregate loss of claims. The posterior distribution for the parameters of severity claims in the risk model is obtained with the implementation of MCMC for the number of mixture random components. The goodness of fit for model is verified with WAIC and DIC Bayesian criteria, after we will compare with cross-validation the results of frequency and severity of claims with the classic risk models. The objective is showing if these results are more efficient with the proposed Bayesian model when we forecast and we verify the mean square error and mean absolute percentage error into cross validation. The methodology is illustrated by the dataCar claims dataset in the insuranceData library of the R statistical software.