Empirical Bayes credibility for the classic Markov chain life insurance setting

Specialeforsvar ved Christian Furrer

Titel: Empirical Bayes credibility for the classic Markov chain life insurance setting 

Abstract: We study inference 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 for the time homogeneous case general expres-sions for the minimum mean square error estimators and the (unconditional) marginal likelihood under right-censoring. Furthermore, 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. We also outline the extension to the time inhomogeneous case. Finally, by considering a model for group disability insurance with piecewise constant transition intensities, we illustrate how the concepts can be applied in actuarial practice. 

Vejledere: Mogens Steffensen, Kristian Buchardt, PFA
Censor:     Alexander Sokol, Nordea