Abstract
Almost all life and health insurance models in the actuarial literature use either a Markov assumption or a semi-Markov assumption. This paper shows that non-Markov modelling is also feasible and presents suitable numerical and statistical tools for the calculation of prospective and retrospective reserves. A central idea is to base the calculation of reserves on forward and backward transition rates. Feasible estimators for the forward transition rates have been recently suggested in the medical statistics literature. This paper slightly extends them according to insurance needs and newly introduces symmetric estimators for backward transition rates. Only few adjustments are actually needed in the classical insurance formulas when switching from Markov modelling to as-if-Markov evaluations in order to avoid model risk.
Highlights
Markov and semi-Markov modelling is the predominant approach in life and health insurance, even though there are numerous examples where the Markov assumptions are not satisfied
Concerning the numerical issues, we show that non-Markov modelling is not harder than Markov modelling if actuarial reserves are calculated based on suitable forward and backward transition rates
We develop a symmetric estimator for the backward transition rates, which are needed for the calculation of retrospective reserves
Summary
Markov and semi-Markov modelling is the predominant approach in life and health insurance, even though there are numerous examples where the Markov assumptions are not satisfied. Concerning the numerical issues, we show that non-Markov modelling is not harder than Markov modelling if actuarial reserves are calculated based on suitable forward and backward transition rates. Christiansen of forward transition rates is feasible by means of the so-called landmark Nelson–Aalen estimator, which was recently suggested in the medical statistics literature. Putter and Spitoni [12] introduced a so-called landmark Nelson–Aalen estimator that extends the concept of the Nelson–Aalen estimator to right-censored non-Markov data This landmark Nelson–Aalen estimator estimates a specific class of forward transition rates. Buchardt et al [2] define artificial forward rates that are meant for efficient numerical computations of prospective reserves Their aim is to use the classical formulas for non-Markov data, whereas we suggest to adjust the classical formulas.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
