2018/10/31 by Kristian Buchardt, K. Buchardt, C. Furrer +6
Economics, Econometrics and Finance · Health Professions · Mathematics · Social Sciences · #60J27 #60J28 #60J75 #91B30 #91G40 #FOS: Economics and business #FOS: Mathematics #Global Health Care Issues #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60J27 #msc:60J28 #msc:60J75 #msc:91B30 #msc:91G40 #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1811.00137
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
openalex publication_date 2018/10/31 · arxiv created 2019/04/01 · arxiv updated 2019/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.