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Abstract:
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In life insurance, mortality is an extremely rare event so that commonly used binary regression models with link functions such as logit, probit and complementary log-log are unable to handle the resulting imbalance. In this paper, we explore the benefits of utilizing a Bayesian framework to the generalized linear models using three proposed link function: the generalized extreme value, Weibull and Frechet. We find that this approach helps us better explain the extreme imbalance. We not only use the link functions to describe how the mean of response variable depends on the linear predictors, but we also use the shape parameter and the mode of the proposed distributions to estimate the skewness or imbalance. For Bayesian model selection and comparison, the Deviance Information Criterion (DIC) has been used. To calibrate our proposed models, we use a real dataset of the mortality experience drawn from a portfolio of a large insurance company. When evaluating the predictive power of our proposed models, they outperformed traditional GLMs.
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