STOCHASTIC MODELING OF VEHICLE INSURANCE CLAIMS: AN APPLICATION IN THE SOUTH OF MINAS GERAIS/BRAZIL
Conteúdo do artigo principal
Resumo
Fatores de risco e exposi¸cao s˜ao pontos importantes a serem considerados, oferecendo informa¸c˜oes financeiras e atuariais para seguradoras. M´etodos de precifica¸c˜ao s˜ao fundamentados na teoria do mutualismo, possibilitando n´ıveis de indeniza¸c˜ao, custos esperados e a constitui¸c˜ao de reservas montet´arias. O objetivo deste trabalho ´e modelar e analisar a distribui¸c˜ao de indeniza¸c˜oes de seguro de ve´ıculos no sul de Minas Gerais, Brasil. Os dados representam ap´olices com ocorrˆencia de sinistros no ano de 2018. Sob o enfoque Bayesiano, foram considerados os modelos Gama e Lognormal, que possibilitam a modelagem de dados assim´etricos e s˜ao comumente utilizados em modelos de perda. Para o estabelecimento de distribui¸c˜oes a priori, recorreu-se a classe de prioris n˜ao informativas de Jeffreys considerando os dados do primeiro semestre de 2018. O n´ıvel
de informa¸c˜ao foi atualizado, construindo informa¸c˜oes a priori para analisar os dados do segundo semestre. A compara¸c˜ao dos modelos foi realizada a partir do Fator de Bayes e da raz˜ao entre o logaritmo das verossimilhan¸cas marginais, que indicaram o modelo Lognormal mais plaus´ıvel. Posteriormente, foram calculadas m´etricas como a Conditional Tail Expectation (CTE) e os percentis da distribui¸c˜ao ajustada, que permitem avaliar n´ıveis de risco, custos extremos e medidas de gerenciamento de reservas
monet´arias. Ademais, os resultados mostraram a aplicabilidade da inferˆencia Bayesiana na modelagem de dados de seguro, permitindo a inser¸c˜ao de informa¸c˜oes a priori, como o hist´orico de carteiras, e uso de diversas fam´ılias de distribui¸c˜oes.
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