Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/287305 
Year of Publication: 
2021
Citation: 
[Journal:] European Actuarial Journal [ISSN:] 2190-9741 [Volume:] 11 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2021 [Pages:] 441-462
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Life and health insurance
Semi-Markov model
Kolmogorov forward equation
Landmark Aalen–Nelson estimator
Landmark Aalen–Johansen estimator
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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