Investigação da capacidade preditiva de modelos com efeitos aleatórios em GAMLSS: um estudo em dados de seguros de automóveis

Abstract

Automotive vehicles are machines of high relevance as they enable not only mobility for individuals, but also have several other benefits. Regardless of their use, the exorbitant amount of vehicles circulating daily brings some complications, such as the increase in the number of traffic accidents. Insurers joined the vehicle insurance market as a response to the vehicle owners’ necessity for financial insurance. Pricing for this type of insurance can be a difficult matter, since different owners will have different characteristics - which are called risk classes - and will also have different driving behaviors - which are evaluated through the policyholder’s experience. In addition, the characteristics of claim values are difficult to estimate, due to the excess of null values and the occurrence of extreme values. Therefore, the more adaptable and robust a model is, the better the predictions will be. At this occasion, the main objective of this work was to propose a model for the pricing of claims that can encompass this complexity. We use the class of regression models, more specifically, generalized additive mixed models for location, scale and shape (GAMMLSS). The data is longitudinal and refers to customers of a Spanish insurance company, containing some information from auto insurance policies, which were monitored for five years. Two distributions were tested for the response variable with different combinations of predictors, covariates and additive terms. The main findings indicate that the model that considered the experience of the insured generated more precise and more accurate estimates. Also, this model presented a behavior in the predictions that more faithfully represents what happened in reality. The proposed methodology can be easily expanded to other types of insurance.