Experience rating in the classic Markov chain life insurance setting An empirical Bayes and multivariate frailty approach

We consider experience rating in the classic Markov chain life insurance setting. We focus on shrinkage estimation of group effects in an empirical Bayes and multivariate frailty extension, building on ideas from group life insurance and survival and event history analysis. Within this framework, we provide insights regarding the structure of the likelihoods and sufficiency of summary statistics such as occurrences and exposures. Simple shrinkage estimators, given by well-known credibility formulas, are obtained under quadratic loss for mutually independent conjugate Gamma priors. The applicability of these simple shrinkage estimators for disability insurance is illustrated in a numerical example using simulated data.