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Projecting mortality rates using a Markov chain

Spreeuw, J. ORCID: 0000-0002-5838-9085, Owadally, I. ORCID: 0000-0002-0830-3554 & Kashif, M. (2022). Projecting mortality rates using a Markov chain. Mathematics, 10(7), 1162. doi: 10.3390/math10071162


We present a mortality model where future stochastic changes in population-wide mortality are driven by a finite-state hierarchical Markov chain. A baseline mortality in an initial ‘Alive’ state is calculated as the average logarithm of observed mortality rates. There are several more ‘Alive’ states and a jump to the next ‘Alive’ state leads to a change (typically, an improvement) in mortality. In order to estimate the model parameters, we minimize a weighted average quadratic distance between observed mortality rates and expected mortality rates. A two-step estimation procedure is used, and a closed-form solution for the optimal estimates of model parameters is derived in the first step, which means that the model can be parameterized very fast and efficiently. The model is then extended to allow for age effects whereby stochastic mortality improvements also depend on age. Forecasting relies on state space augmentation and an innovations state space time series model. We show that, in terms of forecasting, our model outperforms a naïve model of static mortality within a few years. The Markov approach also permits an exact computation of mortality indices like the complete expectation of life and annuity present values which are key in the life insurance and pensions industry.

Publication Type: Article
Additional Information: © 2022 by the authors. Submitted to Mathematics for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (
Publisher Keywords: mortality forecasting; Markov chain; model calibration; life insurance; pensions
Subjects: G Geography. Anthropology. Recreation > GF Human ecology. Anthropogeography
H Social Sciences > HD Industries. Land use. Labor
H Social Sciences > HM Sociology
Q Science > QA Mathematics
Departments: Bayes Business School > Actuarial Science & Insurance
Text - Published Version
Available under License Creative Commons: Attribution International Public License 4.0.

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