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Speaker: Christian Furrer
We study modeling and estimation for a class of empirical Bayes models which allow for group heterogeneity in the classic Markov chain life insurance setting. Special cases of these models have previously been studied in the actuarial literature. Furthermore, the general class of models is related to the so-called frailty models in the field of survival analysis. For our approach, we consider a portfolio consisting of groups of insureds, and assign to each group a vector of (latent) credibility variables representing the group's unobservable risk characteristics. Applying theory on marked point processes and well-known methods for conditional distributions, we derive general expressions for the minimum mean square error estimators and the (unconditional) marginal likelihood under right-censoring. This allows us to estimate the credibility variable as well as the underlying parameters of the model. Next, we study the particular case where the credibility variables within each group are independent, and for this setting we examine the relation between estimation procedures and credibility structures. Furthermore, when the transition intensities are piecewise constant, we show a link between the empirical Bayes credibility setting and well-known hierarchical generalized linear models. Finally, an outline of the extension to semi-Markov chains is given, and by considering a model for group disability insurance, we illustrate how the concepts can be applied in actuarial practice.