On the calculation of prospective and retrospective reserves in non-Markov models. (English) Zbl 1482.91180
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.
Reviewer: Emilia Di Lorenzo (Napoli)
MSC:
| 91G05 | Actuarial mathematics |
Keywords:
life and health insurance; semi-Markov model; Kolmogorov forward equation; landmark Aalen-Nelson estimator; landmark Aalen-johansen estimatorReferences:
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