Stochastic Modeling of Vehicle Insurance Claims: An Application in the South of Minas Gerais/Brazil

Abstract

Risk and exposure factors are important features to be considered, providing financial and actuarial information for the insurer. Pricing methods aresupported by the mutualism theory, ensuring a level of indemnity and expected cost, making possible to constitute monetary reserves. The aim of our paper is to model and analyze the distribution of vehicle insurance claims in the south of Minas Gerais/Brazil. The data represents policies with a claim occurrence in the year of 2018. Under theBayesian approach, we consider the Gamma and Log-normal distributions that allow asymmetric data modeling and they can be used in loss models. The Jeffreys’s prior class was applied considering the data of the first semester of 2018. The information level was updated to construct an informative prior to analyze the data of the secondsemester. To compare models, we estimated the Bayes Factor and the logarithm of the marginal likelihood, that showed the Log-normal more likely. After selecting a model, we estimate metrics as the Conditional Tail Expectation (CTE) and the percentiles of the adjusted distribution to evaluate extreme costs. The results showed the applicabilityof Bayesian inference to fit insurance data, allowing to insert prior knowledge as the portfolio experience and to use a wide class of probability distributions.