  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.
