Discussion on “Experience rating in the classic Markov chain life insurance setting: an empirical Bayes and multivariate frailty approach” (Furrer)

Excerpt

There is always a trade-off between simplicity and efficiency when estimating several transition rates simultaneously. It has become folklore in actuarial science that, for experience rating, each actuarial decrement can be estimated independently of each other (“marginal approach”) using a Poisson regression model and that a summary of exposure time and number of claims for a selection of risk factors is sufficient for this task. The article clearly recapitulates this result in the case where transition rates are independent and distinctly parameterized. More importantly, the article delivers an extension to the not so obvious case where the transition rates are (jointly) dependent on a latent process. As sufficient conditions the author discovers the so called “three points of transition entanglement”. The author further provides a (mathematical) construction of a “distinguisher” that guarantees that these three points are satisfied. Under additional assumptions, this leads to a Poisson–Gamma mixture distribution that provides a generalization of the “classical” Poisson case and thus a starting point to go beyond the marginal approach. …