The Φ-martingale

The COVID-19 pandemic, along with other major pandemics such as HIV/AIDS and the 1918 influenza pandemic, has highlighted critical challenges and opportunities that continue to reshape global perspectives and responses. These events have also had notable implications for the actuarial profession, affecting all practice areas. Drawing from its work on pandemic-related issues, the International Actuarial Association (IAA) has identified several key themes that have emerged from examining the effects of pandemics on actuarial practice. To address these, the IAA’s Pandemic Task Force and the Mortality Virtual Forum have produced four key papers: - Lessons Learned from Pandemics - Implications of COVID-19 Protection Gaps - Implications of COVID-19 Data and Pandemic Modeling (to be released in Q1 2025) - Excess Deaths Analysis: A technical paper reviewing mortality data from 21 countries and exploring various methods for calculating excess deaths. This session aims to provide an overview of the IAA’s pandemic-related initiatives, foster understanding of the implications for the actuarial profession, and promote dialogue on the lessons learned from these global health crises and how the profession could prepare for the future.

Several stochastic mortality forecasting techniques, such as the Lee-Carter and Li-Lee models, extract a time-dependent mortality index from logarithmic mortality rates, while producing a residual noise term. These models typically forecast the index while discarding the noise. However, residuals may contain significant temporal, spatial, and spatio-temporal autocorrelation, offering valuable patterns that can be leveraged to improve forecasts. In this study, we propose a machine learning methodology to incorporate this autocorrelation into the mortality index and its forecasts. We introduce two hyperparameters: one regulates the strength of the enhancement, and the other specifies the adjustment method for the mortality index. The adjusted index can then be forecasted using traditional methods such as random walk, ARIMA, and vector autoregression, or more advanced techniques like spatial dynamic panel linear models, eigenvector spatio-temporal filters, and spatio-temporal ARIMA models. Special care is taken to ensure coherence in forecasts across multiple populations, particularly for the Li-Lee model. We apply the proposed methods to data from several countries, testing them on both the Lee-Carter and Li-Lee models. By optimizing the hyperparameters through a train-test-validation split, we compare forecasts with and without incorporating autocorrelational patterns. The results demonstrate that traditional models can be significantly improved by including this additional information. These refined forecasts offer substantial benefits for applications such as life insurance, annuities, pensions, and other areas dealing with longevity risk.

As younger cohorts increasingly purchase insurance in the post-digital era, understanding the factors behind their life and health insurance decisions becomes crucial for the industry’s strategic positioning. This joint consumer survey by the SOA and SCOR Digital Solutions explores the behavioral factors influencing insurance purchase decisions among Gen Z and Millennials (18-42 years old). Offering a forward-looking analysis, the study utilizes a rich dataset spanning 22 markets across six continents. Utilizing both traditional economic regression and state-of-the-art machine learning models, the research provides a dual analytical perspective on emerging market behaviors and evolving purchasing trends. Beyond a comprehensive array of traditional demographic factors such as age, sex, insurance knowledge, income, etc., the report examines how these generations are embracing online platforms, wearable devices, and lifestyle factors influencing recent insurance purchase behaviors.

Accurate risk assessments are critical to the profitability of life insurers, with medical examina-tions playing a vital role in evaluating applicants’ health risks. While increasing medical exami-nation coverage enhances assessment accuracy, it also increases operational costs and prolongs assessment time. A proven approach to address this issue is to use predictive models to classify applicants based on risk and focus medical examinations on high-risk applicants. This study compares two gradient-boosted tree models – the specifically tailored models and the general-purpose models – that predict risk defined as hospitalization days in a five-year period. The specifically tailored models were trained on over 400,000 contracts from 2015 to 2017, em-ploying the sliding window method to detect characteristics related to risks. In contrast, the general-purpose models were trained on data from 4 million policyholders as of 2015, suitable for various use-cases like applicant assessment and marketing. Three metrics – relative ratios in hospitalization days, health abnormality rate, and claim ratio – were used to evaluate models’ performance. Our findings suggest that the general-purpose models capture a broader represen-tation of the population due to their larger dataset and more balanced target variables. On aver-age, they perform 28% better than the specifically tailored models across the aforementioned metrics. Furthermore, the wider applicability of the general-purpose models reduces the need to train multiple models for different business scenarios, aligning with sustainability goals. There-fore, the general-purpose models outperform the specifically tailored models in medical exam-ination sampling.