Forward transition rates

TY - JOUR

T1 - Forward transition rates

AU - Buchardt, Kristian

AU - Furrer, Christian

AU - Steffensen, Mogens

PY - 2019

Y1 - 2019

N2 - The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalisation 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.

AB - The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalisation 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.

KW - Doubly stochastic Markov models

KW - Forward rates

KW - Kolmogorov forward equations

KW - Life insurance

UR - http://www.scopus.com/inward/record.url?scp=85067413180&partnerID=8YFLogxK

U2 - 10.1007/s00780-019-00397-0

DO - 10.1007/s00780-019-00397-0

M3 - Journal article

AN - SCOPUS:85067413180

SN - 0949-2984

VL - 23

SP - 975

EP - 999

JO - Finance and Stochastics

JF - Finance and Stochastics

IS - 4

ER -