Quantifying uncertainty in survival outcomes is fundamental to demographic and actuarial research. In this context, entropy offers a rigorous framework for capturing the underlying dynamics of mortality. This study investigates how entropy can be used to characterize uncertainty and predictability in survival outcomes, with particular relevance to longevity risk assessment. We propose entropy measures derived from small perturbations to the survival function and interpret them within the additive mortality framework, a flexible class encompassing many widely used mortality models. This approach allows us to examine how entropy reflects age-specific mortality dynamics and long-term trends. Through numerical illustrations based on empirical data, we demonstrate that entropy-based measures provide meaningful insights into the structure and evolution of mortality, offering a complementary perspective to traditional actuarial tools and deepening the understanding of survival uncertainty.

Abstract This paper develops a theory of when annuitization improves or reduces social welfare. The analysis is based on a small open economy with exogenous prices, populated by overlapping generations of non‐altruistic agents. Annuities provide longevity risk insurance and above‐market returns, but also reduce accidental bequests that transfer resources from the old to the young. I show that the welfare trade‐off between these channels is governed by the interest rate: above a threshold, the cost of reducing bequests dominates and no annuitization is socially optimal; below it, partial annuitization improves welfare. Socially optimal allocations can be implemented by mandating a savings portfolio with a predetermined share invested in annuities. Governments that instead mandate annuities through fully funded pensions cannot replicate these allocations, even when annuity markets are missing and agents cannot borrow against future benefits. Although derived for small open economies, the results provide a benchmark for identifying when annuitization raises or lowers welfare and presumably extend to closed economies, where the boundary may still depend on the rate of return but now through threshold values of the parameters that determine it.

Abstract The vast majority of researchers, actuaries, and demographers use standard time series analysis techniques to project time-varying parameters of popular mortality forecasting methods such as the Lee–Carter and Li–Lee models. However, spatial dependence can be as significant as temporal autocorrelation in these time series, and the underlying panel structure of the data is often neglected. We draw on techniques from panel and spatial econometrics, including ordinary and spatial dynamic panel linear models, spatiotemporal autoregressive integrated moving average processes, and spatial eigenvector filters, to capture such dependence and improve projections. We present a methodology to estimate the parameters of these techniques from spatial multipopulation mortality series, select their optimal hyperparameters, and use them for forecasting. We propose a tailor-made robust selection framework to identify the best model–technique combinations for each country, as well as a bootstrap-based procedure to quantify projection uncertainty with accurate nominal coverage on a separate validation period and a strategy for assessing the quality of the resulting prediction intervals. We test these methods on mortality data from 22 European countries. The results show that the proposed techniques yield a clear advantage in both point and interval forecasts for several populations, and these findings are corroborated by a robust selection design and additional robustness checks. These improvements have the potential to deliver meaningful gains for life insurance, pensions, and other contexts involving longevity risk.

Guaranteed annuity options (GAOs) allow policyholders to convert accumulated funds into life annuities at maturity at a guaranteed minimum rate. Thus, insurers are exposed to both investment and longevity risks. Accurate valuation of these long-term, survival-contingent contracts is essential for solvency assessment and risk management. Many existing approaches assume independence between interest rate and mortality risks. This paper develops a computationally efficient pricing framework for GAOs that jointly models interest and mortality rates as correlated stochastic processes with regime-switching dynamics governed by a finite-state continuous-time Markov chain. Model parameters are estimated using U.S. interest rates and cohort mortality data via quasi-maximum likelihood estimation. A semi-analytic valuation formula is derived based on the joint distribution of the underlying processes. Numerical results show that incorporating correlation and regime-switching materially increases GAO prices relative to conventional one-state models. The proposed semi-analytic approach delivers substantial computational advantages over standard Monte Carlo simulations. Sensitivity analysis further identifies the parameters most relevant for long-horizon pricing and solvency considerations. This highlights the practical relevance of the framework for managing longevity-linked guarantees under economic and demographic uncertainty.

Purpose This study aims to synthesise life insurance technology adoption (LITA) research through bibliometric analysis to map its intellectual foundations, thematic clusters and evolution over time. Design/methodology/approach This study follows a bibliometric research design guided by the Scientific Procedures and Rationales for Systematic Literature Reviews (SPAR-4-SLR) protocol. A total of 843 peer-reviewed journal articles, published between 2000 and 2024, indexed in the Scopus database, were analysed. Performance analysis was used to examine trends in publication and citation. In contrast, science-mapping techniques, including keyword co-occurrence analysis, conceptual structure and bibliographic coupling, were applied using Bibliometrix and VOSviewer to explore thematic development and intellectual structures. Findings The analysis reveals a sustained evolution of LITA research, identifying seven interrelated thematic clusters that define the field’s intellectual structure. These clusters focus on actuarial valuation and life insurance liabilities, mortality and longevity risk modelling, solvency and risk return management, customer relationship management and value creation, portfolio choice and lifecycle behaviour, insurance market development and economic growth and micro-level insurance adoption and intermediary dynamics. Overall, the findings show a gradual shift from traditional actuarial foundations towards digitally enabled, data-driven and insurtech-oriented research perspectives. Originality/value This study contributes to the field by integrating fragmented LITA research into a coherent bibliometric framework that highlights key themes, intellectual foundations and emerging research directions.

. Recent regulatory overhauls in North America and Europe require insurers the detailed revision of capital requirements across multiple insurance product domains. These cover unique challenges akin to guaranteed minimum benefits in variable annuities and risk correlations. This article addresses the urgent need to establish robust pricing methodologies for option-embedded guarantees. Our focus is on the pricing of a guaranteed annuity option (GAO), which offers investors with both growth prospects and downside protection. We propose a stochastic correlation framework to capture the dynamic dependence between financial and longevity risks. When the traditional Monte-Carlo method is used as a baseline, our change of probability measures approach not only generates accurate GAO values but also features a remarkably efficient computation. An analysis of the magnitude and direction of the impact of the model parameters on GAO prices is also presented. Both the theoretical and applied contributions of this article have central importance to insurers and regulators alike and to the concerted efforts in sustaining the insurance sector’s stability and consumer protection.

Abstract Longevity risk significantly impacts the reserve adequacy ratio of annuity issuers, thereby reducing product profitability. Effectively managing this risk has thus become a priority for insurance companies. A natural hedging strategy, which involves balancing longevity risk through an optimised portfolio of life insurance and annuity products, offers a promising solution and has attracted considerable academic attention in recent years. In this study, we construct a realistic portfolio scenario comprising annuities and life insurance policies across various ages and genders. By applying Cholesky decomposition, we transform the portfolio into an uncorrelated linear model. Our objective function minimises the variance in portfolio value changes, allowing us to explore the impact of mortality on longevity risk mitigation through natural hedging. Using actuarial mathematics and the Bayesian MCMC algorithm, we analyse the factors influencing the hedging effectiveness of a portfolio with minimised variance. Empirical findings indicate that the optimal life-to-annuity ratio is influenced by multiple factors, including gender, age, projection period, and forecast horizon. Based on these findings, we recommend that insurance companies adjust their business structures and actively pursue product innovation to enhance longevity risk management.

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The ongoing demographic changes present many challenges to modern pension systems, particularly in Poland, where supplementary savings mechanisms have been introduced to increase future retirement benefits. While annuities are the only instruments guaranteeing protection against longevity risk, their adoption remains limited. This phenomenon is known as the “annuity puzzle.” Our study examines Polish pre-retirees’ attitudes toward annuitisation, focusing on behavioural and contextual factors influencing decisions about pension capital distribution. The research is based on focus groups with participants from academic environment aged 50 and above. Findings highlight low economic awareness, limited understanding of annuities, and a preference for flexible capital management. Key deterrents to annuity adoption include risk aversion, inheritance motives, and a distrust of financial mechanisms. Behavioural insights reveal loss aversion, with participants perceiving the potential loss from early death outweighing the benefits of longevity protection. The study underscores the importance of tailored financial education and independent pension advisory services. It advocates for a gradual annuitisation model that balances flexibility with security, addressing psychological barriers and financial realities. The results also call for systemic interventions, including behavioural nudge and simplified communication from financial institutions, to foster a viable market for annuities in Poland.

Population forecasting is critical for actuarial practice, particularly in assessing longevity risk, pricing life annuities, and evaluating pension fund sustainability. Traditional cohort component methods face dimensionality challenges when projecting age- and gender-specific populations for large countries with limited data. In this work, we propose a Factor-augmented Cohort Component Method (FaCCM) that integrates time-varying Leslie matrices with factor modeling to generate mid-to-long-term probabilistic forecasts. Unlike existing approaches, our method requires only census data, avoids restrictive parametric assumptions, and quantifies uncertainties via bootstrapped prediction intervals, which is crucial for actuarial applications such as measuring pension deficits and designing cohort-specific annuities. We validate the FaCCM's performance using simulations and real data, and demonstrate its ability to interpret latent factors driving changes in fertility (e.g. delayed childbearing), improvements in mortality, and shifts in migration patterns. Finally, we apply the FaCCM to China's aging population, projecting demographic shifts through 2060 and quantifying the financial impact of the 2025 retirement delay policy. Our analysis reveals that raising the retirement age to 63 for men and 58 for women reduces the old-age dependency ratio by 15% by 2040, yet is insufficient to stabilize the pay-as-you-go pension expenditures.

Abstract Low-and middle-income countries are experiencing rapid aging, yet participation in pension programs remains stagnant due to widespread informal employment, posing a significant fiscal challenge. Some advocate for improving pension program design to boost contributions, while others support universal, noncontributory pensions. This study examines recent academic literature on the factors influencing active participation in pension systems within high-informality contexts. Emerging evidence indicates that participation is significantly influenced by both financial incentives and nonfinancial barriers. Simultaneously, pensions are not perfect substitutes for other strategies to mitigate longevity risk, such as family support, which will continue to be vital for many older individuals in fiscally constrained settings. Consequently, policymakers should consider integrating contributory pensions, social pensions, and policies that support other forms of elderly care, while examining how these elements interact. To guide these efforts, it is essential to systematically investigate these interactions and expand empirical evidence beyond a limited number of middle-income countries.

Abstract This essay coins and develops the concept of Longevity Capitalism, a biopolitical and financial regime in which both the condition of living longer and the pursuit of longevity are transformed into frontiers of accumulation. As financialisation extends into the domain of ageing, longevity – once a social and fiscal challenge – has been reframed as an investment opportunity. The essay traces a shift from collective welfare management to individualized risk-bearing, showing how uncertainty about life expectancy is converted into a new asset class. Drawing on examples such as financial instruments that profit from longevity risk, the rise of ‘age-tech’, and Silicon Valley’s ventures in life extension, it shows how biological time is increasingly treated as an economic resource. It also examines the speculative pursuit of ‘longevity escape velocity’, where technological innovation is imagined to outpace ageing and death itself becomes a technical problem. Together, these developments reveal a system in which longer life functions as a perpetually deferred investment cycle – an economy sustained by its own postponement. The essay argues that economic and biological time, wealth and health, are now fused within a single regime of managed futurity, reflecting new forms of power over who – and how – gets to live longer.

Modeling mortality rates through hierarchical clustering for three-way data

Abstract Financial products such as annuities, life insurance, and disability insurance are positioned to play a key role in future planning, including retirement, by providing financial security; hedging against different kinds of financial risks, including illness, injury, or death; and maintaining a steady income stream throughout older age. A national online survey of employed American adults ages 25 to 67, with medium to high income or investable assets, explored consumers’ sense of preparedness for their financial futures and lives in older age. Items included people’s overall financial well-being; attitudes toward and usage of various financial products; attitudes toward different longevity risks; and expectations for retirement. Data on demographic characteristics, recent and anticipated life events, and behavioral characteristics such as risk attitudes and optimism were also gathered to allow for multidimensional comparisons. Preliminary results indicate that while concerns around costs related to health conditions and disability, income stability, and spending flexibility are prevalent among consumers, adoption rates for annuities and disability insurance remain low. Across the three products covered in the survey, usage was significantly correlated with knowledge of and familiarity with the product. Many people were learning about these products from informal sources such as family and friends, and through internet searches, rather than from financial institutions or employers. This presentation will provide a comprehensive look into how different financial products and concerns to manage different longevity risks fit into people’s future planning, and how people’s preferences and experiences differ by their family situation or by individual characteristics.

As Malaysia’s population ages, understanding the financial implications of longevity risk and chronic illnesses among the older population is increasingly important. This study investigates how longevity risk interacts with selected chronic illnesses among older Malaysians using a multiple-state annuity model. First, the study explored the mortality and morbidity risks of selected chronic illnesses affecting older Malaysians. This research employed actuarial modeling techniques, including the Markov chain model, the Lee–Carter model, and the age-period-cohort (APC) model. The Markov chain model estimated the likelihood of health transitions, while the Lee–Carter model and the APC model were employed to project mortality and morbidity rates. These models offer a comprehensive framework to assess the longevity risk and financial pressures associated with managing chronic illnesses in aging populations. Second, the projected rates were utilized in the retirement annuity pricing models. There were two multiple-state annuity pricing models considered, one with only healthy and dead states, and the other included chronic illness states. Overall, increased longevity resulting from ongoing improvements in mortality will raise the cost of annuities for a predetermined annuity payment at the compulsory retirement age. By contrast, the inclusion of chronic illness risk in annuity pricing reduces the cost of an annuity for retirees. Hence, the risks of longevity and chronic illness will be taken into account to fairly price retirement-linked products such as annuities.

Measuring and promoting healthy aging at an individual level remains challenging as promoting healthy longevity requires real-time, personalized tools to assess risk and guide interventions in clinical practice. This study aimed to develop and validate a novel Healthy Longevity Index (HLI) for use in primary care settings in older adults. Using data from the Taiwan Longitudinal Study on Aging (TLSA; n=4470), we developed a nomogram-based HLI incorporating demographics, lifestyle factors, intrinsic capacity (IC) measures, and chronic conditions to predict 4-, 8-, and 12-year disability- and dementia-free survival (absence of physical disability, dementia, or mortality). The HLI was internally validated in a TLSA subset and externally validated in the Japanese National Institute for Longevity Sciences, Longitudinal Study of Aging (NILS-LSA) cohort (n=1090). The 12-year HLI nomogram demonstrated robust performance, with C-statistics of 0.79 (bootstrapped 95% CI 0.78-0.80) in the TLSA training cohort and 0.77 (bootstrapped 95% CI 0.75-0.79) in the TLSA validation cohort. External validation in the NILS-LSA yielded a C-statistic of 0.71 (bootstrapped 95% CI 0.66-0.76). The HLI effectively stratified participants into risk tertiles, with the highest-risk group showing only 27.8% probability of 12-year disability- and dementia-free survival compared to 87.8% in the lowest-risk group. Key predictors included age, sex, education, and, particularly, IC impairments in locomotion, visual acuity, and cognition-all assessable during routine primary care consultations. The HLI provides a practical tool for real-time, personalized assessment of healthy longevity risk in primary care settings. Its design enables providers to deliver person-centered care through targeted interventions and individualized prevention strategies that promote healthy aging across populations, especially in older adults.

In developed countries such as Spain, where the population is increasingly aging, retirement planning and longevity risk represent major societal challenges. In Spain, in particular, a significant proportion of household wealth is concentrated in real estate, primarily in the form of owner-occupied housing. For this reason, one emerging financial product in the retirement savings space is the reverse mortgage (RM). This study examines the determinants of acceptance of this financial product using survey data collected from Spanish individuals. The intention to take out an RM is explained through performance expectancy (PE), effort expectancy (EE), social influence (SI), bequest motive (BM), financial literacy (FL), and risk (RK). The analysis applies machine learning techniques: decision tree regression is used to visualize variable interactions that lead to acceptance; random forest to improve predictive capability; and Shapley Additive Explanations (SHAP) to estimate the relative importance of predictors. Finally, Importance–Performance Map Analysis (IPMA) is employed to identify the variables that merit greater attention in the acceptance of RMs. SHAP values indicate that PE and SI are the most influential predictors of intention to use RMs, followed by BM and EE with moderate importance, whereas the positive influence of RK and FL is more reduced. The IPMA highlights PE and SI as the most strategic drivers, and RK and BM act as relevant barriers to the widespread adoption of RMs.

Avoiding a longevity catastrophe: Harnessing longevity indices to mitigate individual, institutional and systemic longevity risks

Abstract This paper proposes a dynamic longevity risk hedging strategy for smooth survival benefit profiles of group self‐annuity (GSA) schemes in the presence of population basis risk. The fund manager of GSA acts on behalf of fund participants in selecting the optimal hedge. The hedging framework is formulated as a mean‐variance optimization problem, which serves as a theoretical framework for selecting the optimal hedging strategy. The hedging mechanism involves trading standardized longevity‐linked securities dynamically. A semi‐analytic solution to the optimal hedge ratio is derived, which enhances the numerical implementation of the strategy. Furthermore, a risk decomposition method is developed, enabling hedging of various sources of risks, such as longevity and investment risks. Numerical illustrations highlight that the hedging strategy effectively mitigates variability in survival benefits. Meanwhile, a holistic risk management framework utilizing the longevity risk hedging strategy and a target volatility investment strategy increases the fund's return per unit of risk.

Longevity risk, health state transitions, and the demand for insurance