South African Actuarial Journal

Mathematical foundations for a resilient profession and economy

C Economou — 2025-12-22

No abstract.

A multivariate stochastic approach to determine long-term success of SA living annuity portfolios

Andries J. van Niekerk — 2025-07-04

Success rates of living annuities within the South African retirement landscape are examined through portfolio modelling that includes domestic equities, cash, and international exposure, via the S&P 500 index. We define success rates based on Cooley’s framework, emphasising financial sustainability throughout retirement. Our approach incorporates foreign exposure by converting S&P 500 gains to South African Rand, accounting for stochastic foreign exchange rate fluctuations. Additionally, US and South African inflation rates are integrated to assess success rates in real terms, ensuring the impact of inflation on retirees’ income is accurately captured. This study incorporates stochastic correlation and stochastic volatility modelling to capture dynamic asset relationships under varied market conditions. The S&P 500 and JSE Top 40 equities are modelled with stochastic volatility, calibrated through the Efficient Method of Moments (EMM), enhancing volatility estimation for equity assets. These techniques support the analysis of optimal portfolio compositions and withdrawal strategies to maximise annuity success rates, providing evidence-based insights for retirement planning in South Africa.

An analysis of the performance of Stellenbosch University actuarial science students

PG Slattery — 2025-12-22

This paper provides an overview of the qualification process for actuaries in South Africa, in particular the role played by universities and factors which may contribute to the strength of such programmes. An outline of the Stellenbosch University actuarial science offering is provided, covering the qualifications available, admission and progression requirements, the academic staff and teaching methods employed. The performance of the Stellenbosch University students over the past 20 years is analysed. Aspects reported on include enrolments and throughput, module pass rates and exemptions from the Actuarial Society of South Africa’s examinations. The performance of Stellenbosch University students in the profession’s examinations and the time taken by graduates to qualify as Fellow actuaries are also considered.

An actuarial climate index for South Africa

C Marais — 2025-12-22

This article presents the South African Actuarial Climate Index as an intuitive tool to reflect the changing frequency of climate extremes and describes, in detail, the process of constructing the index. The index is briefly compared with its counterparts in other regions, the existing applications of actuarial climate indices are summarised, and further potential implementations of the index are illustrated.

A cost of capital approach to determining the LGD discount rate

J Larney — 2025-12-22

Loss Given Default (LGD) is a key risk parameter in determining a bank’s regulatory capital. During LGD estimation, realised recovery cash flows are to be discounted at an appropriate rate. Regulatory guidance mandates that this rate should allow for the time value of money, as well as include a risk premium that reflects the “undiversifiable risk” within these recoveries. Having extensively reviewed earlier methods of determining this rate, we propose a new approach that is inspired by the cost of capital approach from the Solvency II regulatory regime. Our method involves estimating a market-consistent price (that reflects market information) for a portfolio of defaulted loans, from which an associated discount rate may be inferred. We apply this method to mortgage and personal loans data from a large South African bank. The results reveal the main drivers of the discount rate to be the mean and variance of these recoveries, as well as the bank’s cost of capital in excess of the risk-free rate. Our method therefore produces a discount rate that reflects both the undiversifiable risk of recovery recoveries and the time value of money, thereby satisfying regulatory requirements. This work can subsequently enhance the LGD component within the modelling of both regulatory and economic capital.

How healthcare funders can navigate rapid changes in healthcare knowledge from an actuarial perspective

R Nauhaus — 2025-12-22

Medical knowledge is constantly changing, with new information becoming available, and existing knowledge becoming outdated at a rapid rate. Actuaries are often involved in conversations where funders, such as health insurers, need to make decisions regarding the funding of a newly available technology or treatment. By not approving funding for new treatment options, funders can potentially limit patient access to life-saving treatment. On the other hand, funding ineffective treatments can result in unsustainable financial impacts and perhaps poorer patient health outcomes. This is a challenge faced by healthcare funders worldwide. At the time when funding decisions need to be made, uncertainties exist about the long-term safety and effectiveness of these new treatments, but also about the costs and effect of the treatment, how it affects different patient sub-groups and for which patient sub-groups it is effective. Given this challenge, funders look to actuaries to support funding decisions that balance cost, access, safety and sustainability. It is therefore important for actuaries to understand the nature of the problem and what solutions exist. Several strategies have been developed to help with the evaluation and implementation process. These include health technology assessments, cost-effectiveness analyses, managed entry agreements, including coverage with evidence development, and multi-criteria decision analysis, all of which will be explored in this paper. These strategies aim to address the various categories of uncertainty in the decision-making process and to manage the potential cost impact, with the aim of meeting the funders’ objective of maximising the level of health within the population of interest given a budget constraint. This paper explores the features of these different strategies, their benefits and challenges, as well as learnings where these have been applied in real-world settings. Most of the models are not mutually exclusive and can be used together in various combinations. The literature shows that different decision frameworks can yield divergent funding recommendations, depending on the context and objectives of the funder.

Exploring hybrid annuities, behaviour tax and whether the choice of annuity affects this tax

M Barnard — 2025-12-22

This paper shows how the introduction of a life annuity, as a component in a living annuity, improves income certainty under various return assumptions. It shows that a much lower return is then needed to sustain a client’s retirement income or how the same return can now maintain up to a 40% higher income. The impact that adding a life annuity has on the ability to leave an inheritance now and in the future the impact is also shown. The paper explains how data science can be used to decode investor behaviour with the aim of improving investment outcomes. By using machine learning algorithms, the paper identifies the key drivers of switching behaviour. Clustering algorithms were also used to categorise investors into four switching archetypes where each group exhibits distinct switching patterns. The paper ends by exploring the if choosing a hybrid annuity reduces behaviour tax.

The actuarial valuation of living annuities related to maintenance and accrual in divorce and deceased estate contexts

E Theron — 2025-12-22

Living annuities are frequently encountered in matters related to maintenance and accrual in divorce and deceased estate contexts, yet their valuation remains conceptually unsettled. While valuation methods commonly present a range of drawdown scenarios or reference market values, these approaches often fail to reflect the product’s legal structure, economic purpose, and tax treatment. Responsibility for interpreting different scenarios and selecting a valuation basis often falls to attorneys, fiduciaries or the courts—typically without the support of a clear guiding framework. This paper reframes the problem around intention and entitlement: distinguishing the contractual right to income from any contingent inheritance value. It sets out a framework that grounds valuation in the economic function of the annuity rather than in arbitrary drawdown rates or market values. While the paper focuses on living annuities, the underlying principles offer a broader lens for interpreting pre-retirement funds—and may inform more intentional retirement planning strategies by financial advisers.

IFRS 17: A new lens, but can we compare?

BN Thorpe — 2025-12-22

Given the volume of detailed IFRS 17 disclosures (particularly compared to those provided under IFRS 4), it may be surprising to some that while an attempt to directly compare the results of the disclosure notes may yield interesting insights, it is difficult to be definitive given the allowable areas of judgement. This could lead certain users of financial statements to miss context to the results and potentially draw incorrect comparative conclusions—in direct opposition to the stated intent of IFRS 17. This paper will pay particular attention to a number of seemingly directly comparable disclosure notes common to all insurers with General Measurement Model business, including the following:

— the impact of contracts initially recognised in the period,

— the recognition of Contractual Service Margin in profit and loss for insurance contracts issued, and

— the disclosure of sensitivities relating to the impact on the profit/loss and equity position given changes in risk variables at the end of the reporting period

Interesting insights and potential pitfalls in making direct comparison between the disclosures of industry players are highlighted with the audience asked to consider and comment on the following question: can industry once again play a role to work on meaningful areas of alignment and reasonable compromise to improve the comparability of IFRS 17 for the users?

The convergence of machine learning operations and actuarial control

N Pretorius — 2025-12-22

As machine learning techniques increasingly augment or replace traditional actuarial models, actuaries face new challenges in deploying, monitoring, and integrating these models into business operations. This paper explores the intersection between the Actuarial Control Cycle—a foundational framework in actuarial problem-solving—and the Machine Learning Lifecycle, which underpins modern Machine Learning Operations practices. Through comparative analysis and a practical case study in short-term insurance pricing, we highlight differences between the Actuarial Control Cycle and the Machine Learning Lifecycle, including mention of how solutions are implemented and maintained in practice. While both frameworks share a cyclical, iterative structure focused on problem definition, solution development, and monitoring, the Actuarial Control Cycle lacks explicit guidance on deployment and change management which is critical for operationalising models in modern business solutions. We argue that actuaries can benefit from adopting modern machine learning operations principles to enhance monitoring workflows and improve data processes. The paper concludes with recommendations for integrating modern machine learning operations into actuarial practice, identifying opportunities for cross discipline collaboration, education, and the strengthening of the Actuarial Control Cycle to meet the demands of modern modelling.

Unpacking neutrality and moral responsibility in actuarial practice in the shadow of Section 59 racial and ethnicity discrimination allegations

A Akpan — 2025-12-22

What moral responsibility do actuaries bear for unintended harms when technically accurate, procedurally compliant, and seemingly neutral large dataset models, including advanced algorithms, produce socially unfair outcomes? The dominant view in professional ethics defines responsibility narrowly by limiting it to adherence to laws, standards, codes of conduct, and an individual’s judgement to act with honesty and integrity. The South African Actuarial Society, through its Code of Conduct, follows this definition of responsibility: that the actuary has fulfilled their duty if the model they produce is technically sound, complies with the professional standards and the law, does not directly and unfairly discriminate, and there is no intention to unfairly discriminate directly or indirectly. This proceduralist view of responsibility sidesteps the historical injustices and structural inequities that shape the very datasets on which actuarial models rely. Our position takes seriously the view that algorithmic models are always value-laden and hence not neutral. From this, we conclude that actuaries who work with large datasets and advanced algorithms have a responsibility to understand and disrupt the systemic and structural biases embedded in the data they work with. This disruption would entail orienting one’s model towards substantive ethical ends of equity, justice, and redress for the benefit of historically disadvantaged groups.

Learning to allocate: Self-supervised transformers for constrained optimisation

M Malwandla — 2025-12-22

We present the Resource Allocation Transformer, a deep learning framework that learns portfolio-level relationships directly through attention mechanisms, capturing how assets work together rather than only how they perform individually. Most machine learning approaches to portfolio construction reduce allocation to aggregating independent asset predictions, overlooking the complementarity between assets that drives optimal portfolios. Unlike traditional predict-then-optimise pipelines, or Economic Scenario Generators that separate the modelling of economic variables from the optimisation step, the Resource Allocation Transformer integrates correlation structure and optimisation logic within a single differentiable architecture. The framework learns constraint-satisfying allocations through self-supervised exposure to synthetic optimisation problems, providing a more stable alternative to sequential prediction-optimisation workflows. Empirical validation shows effective transfer learning from synthetic curricula to real Johannesburg Stock Exchange data (2005–2024), with the same trained model handling portfolios of varying sizes and across market regimes without retraining. By directly learning to allocate, the Resource Allocation Transformer establishes a new paradigm for asset allocation that adapts through experience rather than requiring problem-specific recalibration.

Semantic analysis in actuarial risk assessment: A framework for portfolio construction and concentration risk measurement

M Malwandla — 2025-12-22

Traditional actuarial risk assessment relies primarily on historical return correlations to evaluate portfolio concentration and tail risk. However, corporate textual disclosures contain forward-looking information about business models, risk exposures, and strategic similarities that may not be fully captured in historical price relationships. This paper develops a systematic framework for incorporating semantic analysis of corporate disclosures into actuarial risk measurement, demonstrating applications to portfolio construction, concentration risk assessment, and stress testing. Using JSE All Share constituents, we apply natural language processing techniques to extract semantic similarity matrices from corporate narratives across business model, geopolitical, and ESG dimensions. Through shrinkage estimation, we combine these semantic correlations with traditional methods to produce enriched risk measures. Our analysis reveals that semantic correlations identify concentration risks not visible in historical data, with Effective Number of Bets reductions of 75%. The framework provides practical tools for incorporating qualitative corporate information into quantitative risk assessment processes.

Quantifying South African sovereign credit risk: An arbitrage-free method to estimate domestic credit spreads for South African government bonds

J Bisschoff — 2025-12-22

This paper presents a transparent, arbitrage-free framework for extracting an implied survival probability curve from quoted debt prices. Using available market data, a risk-free reference curve, and industry-standard loss-given-default assumptions, we price a selected set of bonds by decomposing their expected cash flows into survival and default states. Each component is discounted using the reference curve and a common survival curve is inferred so that the sum of these components matches the observed market price. The resulting all-in spread reflects the relevant risk premia. Calibration is performed using quoted mid prices, which reduces microstructure noise from bid–ask quoting but does not, by itself, remove liquidity premia. Consequently, the implied spreads should be interpreted as credit-plus-liquidity measures. The methodology is demonstrated by estimating South African sovereign risk using rand-denominated government bond prices from Johannesburg Stock Exchange quoted prices. The South African rand swap curve is used as a proxy for the risk-free rate. While the paper focuses on credit spreads for domestic unsecured sovereign debt, the methodology is generalisable to other listed debt instruments, such as floating-rate notes issued by named counterparties or as baskets within a sector, to construct sector-specific credit-spread term structures. When bid and ask quotes information are available, the methodology can be extended to perform calibration at both ends of the spread to assess the sensitivity of the inferred survival curve. Illustrative examples are included in which bid–ask spreads are computed along the term structure of bond prices to show the calibration process and resulting curves.

In-context learning enhanced credibility transformer

K Padayachy — 2025-12-22

The starting point of our network architecture is the Credibility Transformer which extends the classical Transformer architecture by a credibility mechanism to improve model learning and predictive performance. This Credibility Transformer learns credibilitised classification tokens that serve as learned representations of the original input features. In this paper we present a new paradigm that augments this architecture by an in-context learning mechanism, i.e., we increase the information set by a context batch consisting of similar instances. This allows the model to enhance the classification token representations of the instances by additional in-context information and fine-tuning. We empirically verify that this in-context learning enhances predictive accuracy by adapting to similar risk patterns. Moreover, this in-context learning also allows the model to generalise to new instances which, e.g., have feature levels in the categorical covariates that have not been present when the model was trained—for a relevant example, think of a new vehicle model which has just been developed by a car manufacturer.

Effects of extreme climate events on the morbidity of a sample of medical scheme lives in South Africa

C Smith — 2025-12-22

Climate change is intensifying the frequency and severity of extreme weather events, with profound implications for human health. While evidence on mortality impacts is emerging, the morbidity effects of extreme climate events in South Africa remain less explored, particularly within the insured population. This study investigates the morbidity impacts of extreme temperature events on a sample of medical scheme members across South Africa. Using health claims data for approximately 3.48 million beneficiaries, representing close to 40% of the South African private medical scheme market, over the period 2014–2024 (excluding COVID-19 years), linked with regional temperature data,, this study analyses daily healthcare utilisation patterns across all nine provinces. Two methods are applied: two-dimensional kernel density estimation to explore non-linear associations between temperature extremes and utilisation, and distributed lag non-linear models with multivariate meta-regression to capture lagged effects up to 21 days. Results generally reveal a U-shaped relationship between temperature extremes and healthcare utilisation. Extreme heat is associated with increases in healthcare visits and admissions, particularly for circulatory, endocrine, nephrology, and trauma-related conditions, with the strongest effects observed among members aged 40 and older. Extreme cold is linked to elevated respiratory-related utilisation, with lagged impacts persisting several days post-exposure. A case study of the April 2022 KwaZulu-Natal floods, using precipitation data, shows a sharp decline in healthcare visits and admissions during peak rainfall, reflecting acute disruption to healthcare access and utilisation, followed by a partial rebound as weather conditions normalise. These findings align with international evidence while providing novel South African insights, highlighting the vulnerability of South Africa’s people and the healthcare system itself to extreme climate events. The results underscore the importance of integrating climate-related health risks into actuarial applications. Future research can extend this analysis to the broader population and to other climate-related hazards, including air pollution and drought.

Insuring the uninsurable—the case for pooling arrangements in South Africa

M Botha — 2025-12-22

Private insurance markets sometimes fail to provide the necessary capacity for risks that are unpredictable in nature or are heavily correlated. These can result in enormous simultaneous losses. Where traditional insurance can be offered for such risks, it is often at such a high price that consumers cannot reasonably consider it a solution to their insurance needs. Market failures can also occur due to regulatory restrictions. Globally, (re)insurance pooling arrangements have emerged as an important solution to the challenge of insuring large, complex, or systemic risks that are often too capital-intensive or uncertain for traditional insurance markets to bear alone. These arrangements, which enable insurers and reinsurers to underwrite and manage high-severity risks collectively, have been implemented successfully in global insurance markets. Examples include insurance sectors such as nuclear, terrorism, natural catastrophes, and cyber risk. Both regional sovereign risk pools and industryled initiatives have demonstrated how coordinated underwriting, technical expertise, and shared capital can improve resilience and expand access to insurance solutions in high-risk environments. In South Africa, however, formal pooling structures remain limited. The South African Nuclear Pool is currently the only domestic arrangement in operation that includes more than one insurer in a voluntary association model. The State Assured Special Risks Insurance Association (more commonly known by its acronym SASRIA), which provides specialist risk cover on a coinsurance basis with primary insurer agents, operates in a manner that resembles pooling arrangements. However, it continues to underwrite risks on its own balance sheet and relies on traditional reinsurance to optimise its financial position. Other multi-national pools (eg. in specialist employee benefits) in turn often only have one domestic insurer in a particular market participating in the pool, which is different from pooling arrangements with multiple insurers in a domestic market coordinating underwriting of complex risks. The paper explores how local challenges that limit the adoption of pools can be resolved and the opportunities that pooling arrangements provide. It also highlights the role insurance market participants in South Africa can play in leveraging pooling as a unique insurance solution. Pooling arrangements can offer a collaborative, scalable, and internationally proven solution to address uninsurability challenges in South Africa.