  In this paper, we consider the problem of experience rating within the
classic Markov chain life insurance framework. We begin by investigating
various multivariate mixed Poisson models with mixing distributions
encompassing independent Gamma, hierarchical Gamma, and multivariate
phase-type. In particular, we demonstrate how maximum likelihood estimation for
these proposed models can be performed using expectation-maximization
algorithms, which might be of independent interest. Subsequently, we establish
a link between mixed Poisson distributions and the problem of pricing group
disability insurance contracts that exhibit heterogeneity. We focus on
shrinkage estimation of disability and recovery rates, taking into account
sampling effects such as right-censoring. Finally, we showcase the practicality
of these shrinkage estimators through a numerical study based on simulated yet
realistic insurance data. Our findings highlight that by allowing for
dependency between latent group effects, estimates of recovery and disability
rates mutually improve, leading to enhanced predictive performance.
