Projecting mortality rates using a Markov chain
In terms of forecasting, the model outlined in this study outperforms a naïve model of static mortality within a few years.
Mathematical modeling of mortality trends is becoming a central concern for researchers and practitioners due to its importance for public health planning, social insurance, private life insurance, and pension systems. Accurate mortality forecasts are critical to allocate resources in a timely manner for forward planning. In this context, prolonged life expectancy, also known as longevity risk, poses challenges for the pricing, advance funding and reserving of life insurance and pension schemes, which may require forecasts of up to 50 years ahead. Generally, it is difficult to measure and hedge the effects of mortality improvement on retirement planning. Ideally, the difference between observed mortality and mortality estimates should be negligible. However, over the last few decades, old-age mortality projections have underestimated mortality improvement. In light of this, the study Projecting mortality rates using a Markov chain aims to introduce a new method for population-wide mortality modeling.
This paper discusses a new model of stochastic mortality based on a time-homogeneous continuous-time Markov chain of mortality changes. The model allows for age effects, whereby mortality improvements differentially impact individuals of different ages. To forecast mortality rates, states are added to the Markov chain, and an innovations state space time series model is employed. To the best of the authors' knowledge, such models have not been employed in the mortality forecasting literature.
The authors argue that their model has several major advantages. Firstly, it is flexible: one can create as many states in the Markov model as one sees fit. Computations are still fast, and transparency is not compromised. Secondly, the model can be easily calibrated to real mortality data. Life expectancies and reserves required for life insurance and pensions are also easily computed, without recourse to simulations. Finally, once the forecasting part has been completed, i.e. projections have been made of future changes in mortality, it is straightforward to calculate the exact distributions of key quantities like (future) expectancies of life and fixed-rate annuity present values. Therefore, this model can help practitioners forecast mortality and manage longevity risk more easily.
The paper Projecting mortality rates using a Markov chain is published in Mathematics. The published version of the paper is available for download at City Research Online.