Short biography

(Alasdair) David Wilkie was born on the 22nd March 1934 in Didsbury, Manchester, to two Scottish GPs and brought up in Glasgow and Lancaster. He received a scholarship to Rugby School, where he excelled at Mathematics and Greek, and where he first became aware of the actuarial profession through his mathematics master. In December 1950, aged 16, he won an exhibition to Trinity College, Cambridge, and spent a pre-university year working at the Scottish Widows Fund in Edinburgh, where he first became an actuarial student. At Cambridge, he studied Mathematics, Economics, and English, and learned to fly small planes in the University Air Squadron, which led to two years of National Service in the RAF in 1955–57, in which he got his “wings” training on Vampire jet fighters.

From 1957 to 1985, David worked as an actuary in life insurance. This phase of his career saw positions at Scottish Widows, where he qualified as both FFA and FIA, Swiss Reinsurance in Zurich, and Standard Life in Edinburgh, where he remained for 23 years. His early adoption of computer programing, beginning with a Ferranti Pegasus vacuum-tube computer, underpinned much of his research output during that time. A 57-year association with the Continuous Mortality Investigation (CMI) had started in 1964, and David quickly realized that computers could revolutionize the production of graduated mortality tables. In the 1970s, he brought his computational skills to the production of new indices tracking the performance of British government securities, which continue to this day as the FTSE-Actuaries BGS indices. His best-known work, on stochastic models for investments, the forerunners of modern economic scenario generators (ESGs), also had its origins in this period and led to a seminal paper on what is now known as the Wilkie model (Wilkie, Reference Wilkie1986).

In the second phase of his career, from 1985 until 1996, David worked as a partner and consulting actuary with R. Watson & Sons (now part of Willis Towers Watson). On retirement from Watsons, he resumed a relationship with the Department of Actuarial Mathematics and Statistics at Heriot-Watt University, which had begun with part-time lecturing while he was at Standard Life. Until 2011, he was a Visiting Professor and Research Consultant at Heriot-Watt University. With a former Watsons colleague, he also set up and ran his own specialist company, InQA, producing actuarial software and delivering consultancy. Most recently, he was appointed an Honorary Visiting Professor at the University of York.

His achievements in actuarial science have been recognized by many awards, including the Finlaison Medal of the IFoA in 1986 and gold medals of the Faculty of Actuaries in 1993 and Institute of Actuaries in 1995. He holds honorary degrees from Heriot-Watt University, Waterloo University and City St George’s, University of London. He was awarded the Commander of the Order of the British Empire (CBE) in 1998.

David Wilkie’s contributions to actuarial research

The call for papers invited new research that was connected to any of David’s work or that demonstrated David’s influence on the discipline of actuarial science. Given that David has produced over 160 research papers on a wide variety of topics, this encompassed a large area. We further identified specific themes where David’s contributions have been substantial:

Papers selected for the special issue

In “A compositional approach to modelling cause-specific mortality with zero counts,’’ a paper that was presented at the Wilkiefest conference in April 2024, Dong et al. (Reference Dong, Shang, Hui and Bruhn2025) make a practical contribution to the statistical modelling of mortality. Cause-specific mortality data have a structure dictated by competing risks, which cannot be neglected in their analysis. An approach known as compositional data analysis (CODA), dating back to the work of Aitchison (Reference Aitchison1982), is widely used to address this problem and can be combined with dynamic models of mortality, such as Lee & Carter (Reference Lee and Carter1992), to obtain forecasting models. The authors follow the Lee-Carter approach and describe the resulting model as LC-CODA. However, since CODA employs log-transformation, the methodology cannot be directly applied when the data contain zero counts for some mortality causes, which is often the case. The authors’ main innovation is to incorporate an alpha-transformation, or Box–Cox transformation, of the compositional data to circumvent this problem. In an analysis of cause-of-death time series data from England and Wales and the USA, they obtain promising forecasting results that compare favourably with multinomial logistic regression, an alternative approach that has been used in the actuarial literature.

We selected ``An interpretable neural network approach to case-of-death mortality forecasting’’ by Tanaka & Matsuyama (Reference Tanaka and Matsuyama2025) for inclusion in the special issue, since it also considers cause-of-death mortality forecasting, albeit with a rather different methodology drawn from machine learning. The starting point for their work is the adaptive, penalized tensor decomposition (ADAPT) method of Zhang et al. (Reference Zhang, Huang, Hui and Haberman2023), which decomposes the cause-of-death data into factors for cause, age, and observation year. The latter are then forecast using time series techniques, and the resulting predictions of cause-specific mortality have been shown to be superior to many more established procedures. Tanaka and Matsuyama propose the replacement of the tensor decomposition step in ADAPT with a neural network conforming to what is called a convolutional autoencoder (CAE) architecture. This leads to the extraction of a one-dimensional latent layer, which can again be forecast by time series methods. They argue that this improves interpretability since it yields age sensitivities of cause-specific mortality with respect to a single time-series factor. In a study of Japanese, UK, and German data, their CAE approach is shown to give predictive improvements on ADAPT, despite the relative simplicity of the latent factor.

The paper “A unified Bayesian framework for mortality model selection” by Diana et al. (Reference Diana, Wong Siaw Tze and Pittea2025) was also presented at the Wilkiefest conference. In comparing mortality models that incorporate age, period, and cohort effects, the conventional approach to model selection is to fit each model separately and to use an information criterion such as AIC or BIC to select a single best model for a particular dataset. In contrast, the authors adopt a Bayesian model selection approach in which candidate models are embedded in an overarching modelling framework as sub-models, and identifiers for the sub-models are treated as further parameters to be estimated in the Bayesian paradigm. This results in posterior distributions for the probability of each sub-model, as well as the values of its parameters, and has the advantage that inference about key model quantities, such as mortality rates, can be improved by combining insights from more than one plausible model for the data. The main challenge is constructing a Markov chain Monte Carlo (MCMC) solution to sample from the joint posterior distribution, and the authors propose a reversible jump MCMC procedure that allows the simulation path to move between different sub-models with different numbers of parameters. They apply their methodology to data from 40 countries in the Human Mortality Database and find that large countries with large mortality exposures tend to unambiguously favour the most complex sub-models, while countries with lower exposures tend to show higher uncertainty concerning the best sub-model. They repeat the analysis for models that allow stratification of mortality data by different product types (such as annuities, term assurance, and critical illness cover) and suggest that their Bayesian approach is particularly helpful for overcoming data sparsity issues for some combinations of product, age, and year.

We also selected the paper “Optimal decision-making for consumption, investment, housing and life insurance purchase in a couple with dependent mortality” by Zhang et al. (Reference Zhang, Wei and Wang2025) since many elements come together that echo topics in David Wilkie’s research. On the one hand, the paper belongs to the genre of optimal life-cycle models, which have been widely studied since influential papers by Merton (Reference Merton1969) and Richard (Reference Richard1975). On the other hand, it considers the situation of a married couple whose lifetimes are modelled as dependent, a phenomenon consistently observed in practice. A further feature of the paper is the modelling of investment in real estate assets that are correlated with the stock market. Households may derive income from rental of these assets, or they may access housing wealth through equity withdrawal with reverse mortgages. The couple, or the surviving individual after the first death, has the choice of investing in real estate, taking life insurance, or purchasing a variable annuity, and optimal behaviour is derived under a particular set of model assumptions. The value of the paper lies in the creation of a framework for evaluating strategies and products that are aimed at the needs of retired couples with realistic contemporary decision choices.

The paper “Cancer insurance pricing under different scenarios associated with diagnosis and treatment” by Arik et al. (Reference Arik, Cairns, Dodd, Macdonald, Shao and Streftaris2025) is a very good fit for the special issue for two reasons. First, its focus is on multi-state modelling for critical illness insurance (CII), a topic researched by David, and second, a number of its authors are former colleagues of David from Heriot-Watt University. This paper considers the pricing of two stylized insurance contracts – a CII policy that covers breast cancer (BC) and a life insurance contract that can be purchased with an existing BC diagnosis. Morbidity and mortality risk are modelled using three different approaches: a 4-state industry Markov model documented in Reynolds & Faye (Reference Reynolds and Faye2016); a new semi-Markov model with additional states for premetastatic BC and observed metastatic BC, as well as duration-dependent transition intensities from the premetastatic states; a special case of the semi-Markov model that removes duration dependence and thus becomes Markov. In an analysis of cause-of-death and cancer incidence data from England, the semi-Markov model is shown to accord best with empirical evidence. Net insurance premiums are found to be strongly dependent on the time spent in diagnosed and undiagnosed pre-metastatic BC stages. The paper points the way to improved understanding of stage and age-dependent BC survival rates, as well as the impact of different modelling assumptions on insurance company cash flows.

Boyle & Peng’s (Reference Boyle and Peng2025) paper “Ponzi schemes: a review” was presented at Wilkiefest and provides a fascinating overview of fraudulent schemes in recent history, their common features and differences, as well as modelling proposals for their ultimately catastrophic trajectories. The authors divide Ponzi schemes into two types: large-scale heterogenous schemes with unique investment stories, such as Madoff’s scheme and Allen Stanford’s scheme; smaller-scale homogenous schemes that follow the same investment story and spring up with staggering frequency in both developing and developed economies – the Securities and Exchange Commission prosecuted 376 such schemes in the USA between 1988 and 2012. Notwithstanding this classification, every Ponzi scheme shares, to some degree, the same essential characteristics of the charismatic promoter, the plausible story, the steps taken to build trust, the implausible return promise, and regulatory circumventions. Boyle and Peng survey approaches to the modelling of Ponzi schemes that adopt the consumption and investment paradigm, the same essential approach found in the paper by Zhang et al. (Reference Zhang, Wei and Wang2025) in this issue. To adapt standard economic models, various modifications are necessary. Consumption of wealth goes not only to the promoter but also to early investors; for a period of time, this is balanced by new inflows, but eventually they will be mismatched. True returns are effectively zero, so a fictitious scheme balance may be set up that evolves in parallel to the true balance. For actuaries, an interesting observation is the similarity to pay-as-you-go pension schemes, the important difference being the transparency and state sponsorship of the latter. A further interesting actuarial link discussed in the paper is to susceptible-infected-recovered (SIR) models of epidemics, where the SIR groups can be mapped to potential scheme members, current scheme members, and former members who have already redeemed.

The final paper in this issue, “Pensions and protestants: or why everything in retirement can’t be optimized” by Milevsky & Velazquez (Reference Milevsky and Velazquez2025), was also a contribution to Wilkiefest. It centers on empirical analyses that demonstrate a statistically significant relationship between measures of the health of a region’s pension plan and the fraction of a region’s population identifying as protestant Christians. The reasons for this association are not the principal focus of the article, although context is provided by a survey of historical antecedents for the research, including Weber’s “The Protestant Ethic and the Spirit of Capitalism,” and a discussion of differences of opinion between sociologists and economists concerning the relevance of religion. The analysis draws on international data quantifying the health or quality of a country’s pension system with reference to the Mercer/CFA index which weights measures of the adequacy, sustainability and integrity of the system, and state-level US data, in which the health of a pension plan is measured by the funding ratio of actuarially valued assets to liabilities. In both studies, the analysis is controlled for time-varying variables addressing a region’s ability to fund and sustain its system through household wealth (such as GDP per capita) and static variables addressing other important cultural and regional differences. A variable coding the fraction of individuals identifying as protestant is associated with a significant and non-trivial effect in both cases. Since this is a variable that is out of a region’s control, the authors conclude that more technical measures to improve the quality of pension schemes (e.g. through changes to retirement ages or savings) have their limitations in the face of historically entrenched religious and cultural values.

David Wilkie: “Research I have not done yet”

With its historical observations about the role of Scottish Presbyterian ministers in setting up the world’s first funded pension annuity scheme in 1744, the article by Milevsky & Velazquez (Reference Milevsky and Velazquez2025) offers a segue into David’s reflection on “Research I have not done yet.” David Wilkie shares his name with a number of other prominent Scots in history, including a celebrated painter, an Olympic champion swimmer, and a minister of the Church of Scotland (the father of the painter), who prepared a lifetable and produced a book on The Theory of Interest in the 1790s; the latter’s work is described in more detail in the historical section of David’s article.

In other sections, he gives a personal view of topics in mortality modelling, investment index construction, and stochastic modelling of investments that he believes would merit further investigation. They give a sense of David’s large body of research work and a vivid insight into the intellectual curiosity that continues to drive his interests.