Forward transition rates
Abstract
The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework for the discussion of forward rates. Furthermore, we provide a novel definition with its own logic and merits and compare it with the proposals in the literature. The definition turns the Kolmogorov forward equations inside out by interchanging the transition probabilities with the transition intensities as the object to be calculated.
Cite
@article{arxiv.1811.00137,
title = {Forward transition rates},
author = {K. Buchardt and C. Furrer and M. Steffensen},
journal= {arXiv preprint arXiv:1811.00137},
year = {2019}
}
Comments
Revision of manuscript. The manuscript now contains a section on 'Forward-thinking and actuarial practice'. Furthermore, we have corrected typos and re-written certain sentences to improve readability and accuracy