On the calculation of prospective and retrospective reserves in non-Markov models
type: Item
instance of: scholarly article
title: On the calculation of prospective and retrospective reserves in non-Markov models
zbMATH Open document ID: 1482.91180
author: Marcus C. Christiansen
published in: European Actuarial Journal
publication date: 2022-01-14T00:00:00Z
review text: The paper considers the calculation of reserves on forward and backward transition rates and provides numerical methods based on non-Markov modelling. To this aim, the random pattern of states of an individual life or health insurance policy are depicted by means of a stochastic jump process. After considering the information conditioning on the calculation of prospective and retrospective reserves, the insurance cash flows for both the reserves are defined. Then, an extension of the Kolmogorov forward equation to non-Markov frameworks is presented and the statistical estimation of forward and backward transition rates is treated. Finally, on the basis of the obtained estimators, the calculation of prospective and retrospective reserves is provided. The proofs of all the theorems stated in the paper are in the Appendix.
Mathematics Subject Classification ID: 91G05
zbMATH DE Number: 7457620
zbMATH Keywords: life and health insurance
zbMATH Keywords: semi-Markov model
zbMATH Keywords: Kolmogorov forward equation
zbMATH Keywords: landmark Aalen-Nelson estimator
zbMATH Keywords: landmark Aalen-johansen estimator
reviewed by: Emilia Di Lorenzo
MaRDI profile type: Publication
full work available at URL: s13385-021-00277-y
OpenAlex ID: W3175024178
cites work: Kolmogorov’s forward PIDE and forward transition rates in life insurance
cites work: Forward transition rates
cites work: Dynamics of state-wise prospective reserves in the presence of non-monotone information
cites work: Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models
cites work: Fréchet differentiability, \(p\)-variation and uniform Donsker classes
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cites work: Non-parametric inference of transition probabilities based on Aalen-Johansen integral estimators for acyclic multi-state models: application to LTC insurance
cites work: Forward mortality and other vital rates - are they the way forward?
cites work: State occupation probabilities in non-Markov models
DOI: 10.1007/S13385-021-00277-Y
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description: scientific article; zbMATH DE number 7457620