  The Tweedie generalized linear models are commonly applied in the insurance
industry to analyze semicontinuous claim data. For better prediction of the
aggregated claim size, the mean and dispersion of the Tweedie model are often
estimated together using the double generalized linear models. In some
actuarial applications, it is common to observe an excessive percentage of
zeros, which often results in a decline in the performance of the Tweedie
model. The zero-inflated Tweedie model has been recently considered in the
literature, which draws inspiration from the zero-inflated Poisson model. In
this article, we consider the problem of dispersion modeling of the Tweedie
state in the zero-inflated Tweedie model, in addition to the mean modeling. We
also model the probability of the zero state based on the generalized
expectation-maximization algorithm. To potentially incorporate nonlinear and
interaction effects of the covariates, we estimate the mean, dispersion, and
zero-state probability using decision-tree-based gradient boosting. We conduct
extensive numerical studies to demonstrate the improved performance of our
method over existing ones.
