Hattendorff's Theorem: A Markov chain and counting process approach
- 1 January 1988
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1988 (1-3) , 143-156
- https://doi.org/10.1080/03461238.1988.10413845
Abstract
The paper provides a generalization of Hattendorff's theorem to the situation where a life insurance policy is modelled as a time-inhomogeneous Markov chain with a finite state space. It is shown that the present values of the gains obtained in the different states are zero mean martingales and that gains realized in different states are uncorrelated. Moreover, variance formulas for the present values of the gains are derived, and the results are illustrated by examples relating to term and disability insurance.Keywords
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