Forecasting Futures: AI Meets Actuarial Science in Longevity Risk

by

Author: Denis Avetisyan

A new framework combines the power of deep learning with established actuarial principles to improve the accuracy and interpretability of longevity forecasts.

This paper introduces Hybrid-Lift, a neural-actuarial model designed to address the stationarity paradox and enhance regulatory capital assessment under Solvency II.

Traditional longevity forecasting relies on assumptions challenged by emerging data from high-longevity nations, revealing a systemic mispricing of risk. This is addressed in ‘Neural-Actuarial Longevity Forecasting: Anchoring LSTMs for Explainable Risk Management’, which proposes Hybrid-Lift, a novel framework combining Hierarchical LSTM networks with actuarial principles to improve accuracy and explainability. Our results demonstrate out-of-sample performance gains of up to 17.40% in key markets, alongside an integrated governance suite for regulatory compliance under Solvency II. Could this approach offer a viable pathway towards more robust and transparent longevity risk management in a rapidly evolving landscape?

The Evolving Landscape of Longevity Forecasts

For much of the 20th century, actuaries and demographers relied on models like the Gompertz Law to forecast mortality trends, predicated on the assumption of stationarity – that death rates, while changing over time, did so within a relatively stable range. This allowed for reasonably accurate long-term projections of life expectancy and associated financial calculations, such as those determining pension payouts or insurance premiums. The Gompertz curve, for example, posited an exponential increase in mortality with age, a pattern broadly consistent with observed data for extended periods. This foundational approach facilitated stable planning because it suggested that future mortality improvements would simply continue established historical trends, enabling predictable, if not perfect, assessments of longevity risk. Consequently, a large body of actuarial science and public policy was built upon this principle of relatively consistent, predictable death rates.

Recent analyses of mortality data reveal a compelling, and somewhat unsettling, phenomenon termed the ‘Stationarity Paradox’. For much of the 20th century, death rates appeared relatively stable, allowing demographers to confidently project future trends using established models. However, since the latter half of the 20th century, this stability has eroded. Observed mortality rates now demonstrably shift over time, exhibiting what statisticians call ‘non-stationarity’. This change isn’t random noise; it’s driven by potent forces like advancements in medical technology, public health initiatives, and evolving lifestyle factors – including diet and exercise. Consequently, projections based on the assumption of constant death rates increasingly diverge from actual outcomes, demanding more sophisticated modeling techniques that account for these dynamic, and often unpredictable, shifts in human longevity.

The reliability of long-term mortality projections is increasingly challenged by the discovery of non-stationary trends in death rates. Statistical analysis reveals the presence of ‘Unit Root’ processes within mortality time series – indicating that past death rates are not necessarily predictive of future ones, and that observed trends may not revert to a stable mean. This violates a core assumption of traditional models, like the Gompertz Law, which rely on consistent, predictable changes in mortality. Consequently, standard actuarial forecasts, used for pension planning and insurance risk assessment, become less accurate, potentially leading to significant underestimation of future liabilities. Addressing this requires the development of innovative modeling techniques capable of capturing these dynamic shifts, such as time-varying parameter models and stochastic projections that account for the inherent uncertainty in future mortality experiences.

Modeling Change: A Neural-Actuarial Synthesis

Hybrid-Lift addresses the complexities of non-stationary mortality – mortality rates that change over time – by integrating Long Short-Term Memory (LSTM) networks with established actuarial methods. This framework utilizes LSTMs to capture temporal dependencies in mortality data, while simultaneously employing Mean-Bias Correction (MBC) to mitigate systematic forecasting errors. MBC functions by adjusting model outputs to account for historical biases, effectively improving the calibration of predicted mortality rates. The unique combination allows Hybrid-Lift to model underlying trends and adjust for consistent over- or under-estimation, resulting in more accurate and reliable long-term mortality projections compared to traditional statistical or purely actuarial approaches.

Hybrid-Lift employs a first-differences approach to mortality forecasting, modeling changes in rates rather than absolute levels. This technique calculates the difference between consecutive mortality rates, focusing the model on the incremental shifts that often characterize non-stationary mortality patterns. Empirical results demonstrate that this approach yields a substantial reduction in Root Mean Squared Error (RMSE), achieving a 48.6% improvement compared to models that directly forecast absolute mortality rates. This performance gain is attributed to the increased sensitivity of first-differences modeling to evolving mortality trends and its reduced susceptibility to level-specific errors.

Hybrid-Lift employs Credibility Theory to combine forecasted mortality rate changes – calculated as first differences – with historical data, weighting each based on their respective predictive reliability. This blending process optimizes the balance between model predictions and observed experience, reducing the impact of model error and improving forecast accuracy. Implementation of Mean-Bias Correction further refines the model by systematically removing persistent biases in the predicted changes. Combined, these techniques yield an 18.6% reduction in Root Mean Squared Error (RMSE) compared to models that do not incorporate both Credibility weighting and bias correction.

Quantifying Uncertainty and Validating Model Performance

Hybrid-Lift incorporates Monte Carlo Dropout as a regularization method during both training and inference. This technique involves randomly dropping neurons during each forward pass, creating multiple slightly different model realizations. By averaging the predictions from these realizations, the model generates a distribution of possible outcomes, allowing for the calculation of prediction intervals. These intervals provide a measure of the model’s uncertainty – a quantification of how confident the model is in its prediction – which is crucial for risk assessment and decision-making in actuarial science. The wider the prediction interval, the greater the uncertainty associated with the forecast.

Model performance was evaluated using data from the ‘Frontier Mortality Cluster’, a group of nations characterized by consistently high life expectancies. This testing revealed a quantifiable improvement in forecasting accuracy when compared to baseline models; specifically, the model achieved a 17.40% increase in accuracy for mortality predictions in Sweden and a 12.57% improvement for West Germany. These results demonstrate the model’s capacity to generate more precise predictions within populations already exhibiting extended lifespans, suggesting robustness in scenarios with limited historical data on extreme longevity.

SHAP (SHapley Additive exPlanations) values were calculated to determine feature importance within the mortality prediction model. This method assigns each feature an importance value for a particular prediction, representing the marginal contribution of that feature to the difference between the actual prediction and the average prediction. Analysis using SHAP values revealed that factors such as age, historical mortality rates, and specific socio-economic indicators were consistently the most influential drivers of mortality predictions across the analyzed populations. The resulting feature importance rankings provide insights into the model’s decision-making process, enhancing transparency and allowing for validation of model behavior against domain expertise.

Beyond Prediction: Embracing the Dynamics of Longevity

Traditional mortality modeling, exemplified by the Lee-Carter Framework, often focuses on predicting absolute levels of death rates, a methodology that struggles when faced with shifting historical patterns or unforeseen events. Hybrid-Lift distinguishes itself by instead modeling the changes in these rates – the acceleration or deceleration of mortality trends. This nuanced approach circumvents the limitations of predicting a fixed level, allowing the model to adapt more effectively to non-stationary data and capture the dynamic nature of human lifespans. By concentrating on the rate of change, Hybrid-Lift provides a more flexible and responsive system for understanding and projecting future mortality, offering improved accuracy when historical trends are disrupted and absolute levels are less reliable indicators.

Rigorous testing demonstrates that the Hybrid-Lift model consistently surpasses the predictive power of the Li-Lee Extension, a frequently utilized improvement upon the foundational Lee-Carter Framework. This outperformance is particularly pronounced when analyzing mortality data exhibiting non-stationary trends – situations where patterns of death rates shift over time in a non-predictable manner. While the Li-Lee Extension attempts to capture evolving mortality through added complexity, Hybrid-Lift’s focus on changes in rates, rather than absolute levels, provides a more robust and adaptable approach. Consequently, this model offers more reliable long-term projections in dynamic populations, proving crucial for accurate risk assessment and financial planning where traditional methods fall short.

The refinement of mortality modeling, moving beyond absolute level predictions to focus on rates of change, carries significant ramifications for several critical sectors. Actuarial science benefits from a more responsive tool for assessing financial risks and liabilities, particularly in a world experiencing evolving health trends and demographic shifts. Pension planning, historically reliant on static life expectancy estimates, gains a robust framework for ensuring long-term solvency and equitable benefit distribution. Furthermore, public health policy stands to be informed by projections that dynamically reflect improvements – or deteriorations – in population health, enabling proactive resource allocation and targeted interventions. This adaptable foundation promises not merely more accurate long-term forecasts, but also a strengthened capacity to navigate future uncertainties and build resilience within these interconnected systems.

The pursuit of accurate longevity forecasting, as demonstrated by Hybrid-Lift, isn’t about imposing a grand design, but recognizing patterns arising from inherent interactions. This framework acknowledges the ‘stationarity paradox’ – the challenge of applying static models to dynamic systems – by allowing the LSTM network to learn directly from the data while remaining anchored by actuarial principles. It mirrors the notion that robustness emerges, it’s never engineered. As Georg Wilhelm Friedrich Hegel observed, ‘The truth is the whole.’ Hybrid-Lift, in its synthesis of neural networks and actuarial science, moves closer to capturing that ‘whole’ – a more complete understanding of longevity risk, born not from top-down control, but from the interplay of local rules within the data itself. Small interactions, in this case between the LSTM and actuarial constraints, create monumental shifts in forecasting accuracy.

What Lies Ahead?

The pursuit of longevity forecasting, as demonstrated by Hybrid-Lift, isn’t about conquering uncertainty – that’s a fool’s errand. It’s about navigating a system where apparent stationarity is an illusion, a temporary confluence of forces. The framework offers a valuable step towards reconciling the demands of regulatory capital assessment with the inherent non-linearity of demographic processes, but it doesn’t erase the fundamental challenge: every connection carries influence, and those connections are constantly shifting. Future iterations will inevitably grapple with incorporating broader datasets – genomic information, lifestyle factors, even macroeconomic indicators – not to predict individual lifespans, but to better map the contours of collective risk.

A crucial direction lies in moving beyond point forecasts. The current focus on single values obscures the range of plausible futures. The field needs to embrace probabilistic modeling, quantifying not just what might happen, but how likely each scenario is. This isn’t about achieving greater precision; it’s about acknowledging the inherent fuzziness of the system. Self-organization is real governance without interference; the models should reflect this, allowing emergent patterns to reveal themselves rather than imposing artificial order.

Ultimately, the value of such work resides not in its predictive power, but in its capacity to refine the questions. The goal isn’t to eliminate longevity risk, but to understand its dynamics, to anticipate its propagation through complex systems, and to build resilience in the face of inevitable surprises. The limitations of any model are, after all, a more honest reflection of reality than any illusion of control.

Original article: https://arxiv.org/pdf/2605.06438.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2026-05-09 20:26