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.

Modeling the Risk in Mortality Projections

“…While a number of papers in the mathematical finance literature have discussed frameworks for life-contingent forward rate modeling emphasizing advantages in this arena (Bauer et al, 2012;Tappe and Weber, 2014;Christiansen and Niemeyer, 2015;Buchardt et al, 2019), we are the first to present an empirically derived mortality surface model.…”

Two-dimensional forward and backward transition rates

“…So it turned out that the implicit concept has serious limitations. Buchard, Furrer and Steffensen [2] suggested to overcome these limitations by introducing additional artificial states, but their concept is restricted to insurance contracts that have sojourn payments only and no transition payments. Buchardt [1] discarded the implicit concept and presented an explicit definition that works for a doubly stochastic Markov framework.…”