The popularity of green, social and sustainability-linked bonds (GSS bonds) continues to rise, with circa US$939 billion of such bonds issued globally in 2023. Given the rising popularity of ESG-related investment solutions, their relatively recent emergence, and limited research in this field, continued investigation is essential. Extending non-traditional techniques such as neural networks to these fields creates a good blend of innovation and potential. This paper follows on from our initial publication, where we aim to replicate the S&P Green Bond Index (i.e. this is a time series problem) over a period using non-traditional techniques (neural networks) predicting 1 day ahead. We take a novel approach of applying an N-BEATS model architecture. N-BEATS is a complex feedforward neural network architecture, consisting of basic building blocks and stacks, introducing the novel doubly residual stacking of backcasts and forecasts. In this paper, we also revisit the neural network architectures from our initial publication, which include DNNs, CNNs, GRUs and LSTMs. We continue the univariate time series problem, increasing the data input window from 1 day to 2 and 5 days respectively, whilst still aiming to predict 1 day ahead.

Stochastic mortality models are important for a variety of actuarial tasks, from best-estimate forecasting to assessment of risk capital requirements. However, the mortality shock associated with the Covid-19 pandemic of 2020 distorts forecasts by (i) biasing parameter estimates, (ii) biasing starting points, and (iii) inflating variance. Stochastic mortality models therefore require outlier-robust methods for forecasting. Objective methods are required, as outliers are not always obvious on visual inspection. In this paper we look at the robustification of three broad classes of forecast: univariate time indices (such as in the Lee-Carter and APC models); multivariate time indices (such as in the Cairns-Blake-Dowd and newer Tang-Li-Tickle model families); and penalty projections (such as with the 2D P-spline model). In each case we identify outliers using quantitative methods, then co-estimate outlier effects along with other parameters. Doing so removes the bias and distortion to the forecast caused by a mortality shock, while providing a robust starting point for projections. Illustrations are given for various models in common use.

A common statistical modelling paradigm used in actuarial pricing is (a) assuming that the possible loss model can be chosen from a dictionary of standard models; (b) selecting the model that provides the best trade-off between goodness of fit and complexity. Machine learning provides a rigorous framework for this selection/validation process. An alternative modelling paradigm, common in the sciences, is to prove the adequacy of a statistical model from first principles: for example, Planck’s distribution, which describes the spectral distribution of blackbody radiation empirically, was explained by Einstein by assuming that radiation is made of quantised harmonic oscillators (photons). In this working party we have been exploring the extent to which loss models, too, can be derived from first principles. Traditionally, the Poisson, negative binomial, and binomial distributions are used as loss count models because they are familiar and easy to work with. We show how reasoning from first principles naturally leads to non-stationary Poisson processes, Lévy processes, and multivariate Bernoulli processes depending on the context. For modelling severities, we build on previous research that shows  how graph theory can be used to model property-like losses. We show how the methodology can be extended to deal with business interruption/supply chain risks by considering networks with higher-order dependencies. For liability business, we show the theoretical and practical limitations of traditional models such as the lognormal distribution. We explore the question of where the ubiquitous power-law behaviour comes from, finding a natural explanation in random growth models. We also address the derivation of severity curves in territories where compensation tables are used. This research is foundational in nature, but its results may prove useful to practitioners by guiding model selection and elucidating the relationship between the features of a risk and the model’s parameters.

Paragraph 53(a) of the new insurance accounting standard IFRS 17 suggests there is a relationship between the liability for remaining coverage (“LFRC”) calculated under the general measurement model (“GMM”) and premium allocation approach (“PAA”), although it is not immediately obvious how the two are related or could result in a similar estimate for the LFRC. This paper explores the underlying relationship between the GMM and PAA through the equivalence principle and presents a set of sufficient mathematical conditions that result in an identical LFRC when calculated under the GMM and PAA. An illustrative example is included to demonstrate how the sufficient conditions can be applied in practice and the optimisation opportunities offered to actuaries and accountants when conducting PAA eligibility testing.

The (re)insurance industry is maturing in its ability to measure and quantify Cyber Risk. The risk and threat landscapes around cyber continue to evolve, in some cases rapidly. The threat actor environment can change, as well as the exposure base, depending on a variety of external factors such as political, economic and technological factors. The rapidly changing environment poses interesting challenges for the risk and capital actuaries across the market. The ability to accurately reflect all sources of material losses from cyber events is challenging for capital models and the validation exercise. Furthermore, having a robust enterprise risk management (ERM) framework supporting the business to evaluate Cyber Risk is an important consideration to give the board comfort that Cyber Risk is being effectively understood and managed by the business. This paper discusses Cyber Risk in relation to important risk and capital model topics that actuaries should be considering. It is challenging for the capital models to model this rapidly changing risk in a proportionate way that can be communicated to stakeholders. As model vendors continue to mature and update models, the validation of these models and the ultimate cyber capital allocation is even more complex. One’s view of risk could change rapidly from year to year, depending on the threat or exposure landscape as demonstrated by the ransomware trends in recent years. This paper has been prepared primarily with General Insurers in mind. However, the broader aspects of capital modelling, dependencies and ERM framework are relevant to all disciplines of the profession.

Recent advances in large language models (LLMs), such as GPT-4, have spurred interest in their potential applications across various fields, including actuarial work. This paper introduces the use of LLMs in actuarial and insurance-related tasks, both as direct contributors to actuarial modelling and as workflow assistants. It provides an overview of LLM concepts and their potential applications in actuarial science and insurance, examining specific areas where LLMs can be beneficial, including a detailed assessment of the claims process. Additionally, a decision framework for determining the suitability of LLMs for specific tasks is presented. Case studies with accompanying code showcase the potential of LLMs to enhance actuarial work. Overall, the results suggest that LLMs can be valuable tools for actuarial tasks involving natural language processing or structuring unstructured data and as workflow and coding assistants. However, their use in actuarial work also presents challenges, particularly regarding professionalism and ethics, for which high-level guidance is provided.

This research employs a vector autoregression (VAR) analysis to explore the volatility and dynamic interactions between stock, commodity, and cryptocurrency markets. It focuses on the returns of the S&P 500, gold, crude oil, and Bitcoin to analyse their interconnections. Our results indicate that Bitcoin returns positively affect S&P 500 and crude oil, but negatively impact gold. Conversely, crude oil returns have a positive influence on gold but lead to decreased returns for Bitcoin and the S&P 500. Similarly, higher gold returns correspond to increased returns in crude oil and S&P 500 but decreased returns in Bitcoin. The rise of the S&P 500 negatively influences Bitcoin and crude oil returns, while gold returns remain unaffected. However, these relationships exhibit weak and limited strength. Including these assets in a portfolio can help risk mitigation, as Bitcoin diversifies crude oil, gold, and S&P 500, and crude oil diversifies S&P 500. These findings contribute to our understanding of global financial dynamics and inform decision-making in risk assessment, portfolio management, risk mitigation, and diversification strategies.

The Institute and Faculty of Actuaries UK Asbestos Working Party update 2020 sets out the methodology and assumptions used to estimate the potential cost of asbestos-related claims to the UK Employers’ Liability Insurance Market. The Working Party has estimated the UK EL Insurance Market cost for the following asbestos-related disease types: mesothelioma, lung cancer, asbestosis and pleural thickening, and pleural plaques. For each disease type the Working Party has constructed a range of scenarios to highlight the uncertainty of these estimates. The Working Party reminds practitioners that use the Working Party scenarios that they should always consider the experience and trends that have occurred since the scenarios were published, adjusting the scenarios to take into account new information.

This paper is motivated by the findings of a review in 2020 by the Institute and Faculty of Actuaries, which found that commutation factors differed widely between schemes, they were typically significantly below transfer value factors, and that in nearly 30% of cases, trustees did not act fully on the actuary’s advice. The author suggests that regulation of commutation factors, instead of factors being decided by trustees’ discretion, could be a suitable way forward. The focus is commutation factors for UK-defined benefit pension schemes, having regard to the law that governs the discretion available to trustees. Relevant legal principles are explained, including the requirement for trustees’ decisions to be made for a proper purpose and to be made with due care and skill, taking into account relevant considerations. These principles are applied to the setting of commutation factors. The author describes four methods trustees may use to assess the actuarial equivalence of the pension being exchanged for cash, which is ordinarily part of the process to set commutation factors. None of the four is entirely satisfactory, although it is suggested that there are some advantages in viewing commutation as a transaction between trustees and members. The possible use of market-consistent factors is one of the topics discussed. Commutation factors can also incorporate guarantee charges and/or deductions for underfunding, although the author explains the argument that the latter should not be commonly applied. The role of employers’ and members’ expectations is discussed and can explain why commutation factors can reasonably be less than 100% of actuarial equivalence. It is argued that the impact of commutation on employers’ contributions can in some circumstances justify adjusting commutation factors. The paper also considers other reasons sometimes put forward for reducing factors: tax, utility and optionality. The author also argues that reviewing commutation factors only every three years sits uneasily with legal principles. Further enquiry is suggested as to the responsibilities in law of actuaries when certifying that factors are reasonable. The author suggests that trust law permits trustees to use their discretion in a way that can produce a wide range of outcomes, which may be regarded as unsatisfactory for determining what may be an important part of a member’s reward package, and that a better approach may be for the government to introduce regulations on commutation factors, including a form of disclosure to help inform members’ choice on exercising the option.

The Risk Margin under Solvency II is determined as the cost of holding capital over the lifetime of liabilities, whereby future costs are discounted to the valuation date at risk-free rates. An implicit assumption of the current method is that the Risk Margin should allow for new capital to be raised after the occurrence of losses no larger than required capital. Using “Cost of Capital” as general valuation method, various approaches are discussed, giving rise to several alternative calculation methods of the Risk Margin. A comparison is made with the adjustment proposed by EIOPA in 2020 and also an approach is explored where future capital raisings are treated as contingent commitments. Each of the approaches discussed can be justified on its own merits in the context of Solvency II legislation, and leads to substantially different results for liabilities with long durations. Therefore, a more precise specification of the function of the Risk Margin and underlying assumptions is desirable.

We explore some of the risks related to Artificial Intelligence (AI) from an actuarial perspective based on research from a transregional industry focus group. We aim to define the key gaps and challenges faced when implementing and utilising modern modelling techniques within traditional actuarial tasks from a risk perspective and in the context of professional standards and regulations. We explore best practice guidelines to attempt to define an ideal approach and propose potential next steps to help reach the ideal approach. We aim to focus on the considerations, initially from a traditional actuarial perspective and then, if relevant, consider some implications for non-traditional actuarial work, by way of examples. The examples are not intended to be exhaustive. The group considered potential issues and challenges of using AI, related to the following key themes:

• Ethical

  • ○ Bias, fairness, and discrimination

  • ○ Individualisation of risk assessment

  • ○ Public interest

• Professional

  • ○ Interpretability and explainability

  • ○ Transparency, reproducibility, and replicability

  • ○ Validation and governance

• Lack of relevant skills available

• Wider themes

This paper aims to provide observations that could help inform industry and professional guidelines or discussion or to support industry practitioners. It is not intended to replace current regulation, actuarial standards, or guidelines. The paper is aimed at an actuarial and insurance technical audience, specifically those who are utilising or developing AI, and actuarial industry bodies.

Running off the £2 trillion of UK corporate sector defined benefit liabilities in an efficient and effective fashion is the biggest challenge facing the UK pensions industry. As more and more defined benefit pension schemes start maturing, the trustees running those schemes need to consider what their target end-state will be and the associated journey plan. However, too few trustee boards have well-articulated and robust plans. Determining the target end-state requires a grasp of various disciplines and an ability to work collaboratively with different professional advisers. This paper sets out issues trustees, employers and their advisers can consider when addressing whether their target end state should be low- dependency, buyout or transfer to a superfund. Member outcomes analysis is introduced as a central tool through which to differentiate alternative target end-states. A five-step methodology is set out for deriving an optimal target end-state for a scheme. Also considered are the specific factors impacting stressed schemes, which highlights the importance to trustee boards when considering their Plan B should their employer or scheme ever become stressed. The paper ends with specific recommendations for the actuarial profession and The Pensions Regulator to take forward.

This paper demonstrates workflows to incorporate text data into actuarial classification and regression tasks. The main focus is on methods employing transformer-based models. A dataset of car accident descriptions with an average length of 400 words, available in English and German, and a dataset with short property insurance claims descriptions, are used to demonstrate these techniques. The case studies tackle challenges related to a multilingual setting and long input sequences. They also show ways to interpret model output and to assess and improve model performance, by fine-tuning the models to the domain of application or to a specific prediction task. Finally, the paper provides practical approaches to handle classification tasks in situations with no or only few labelled data. The results achieved by using the language-understanding skills of off-the-shelf natural language processing (NLP) models with only minimal pre-processing and fine-tuning clearly demonstrate the power of transfer learning for practical applications.

The market for green bonds, and environmentally aligned investment solutions, is increasing. As of 2022, the market of green bonds exceeded USD 2 trillion in issuance, with India, for example, having issued its first-ever sovereign green bonds totally R80bn (c.USD1bn) in January 2023. This paper lays the foundation for future papers and summarises the initial stages of our analysis, where we try to replicate the S&P Green Bond Index (i.e. this is a time series problem) over a period using non-traditional techniques. The models we use include neural networks such as CNNs, LSTMs and GRUs. We extend our analysis and use an open-source decision tree model called XGBoost. For the purposes of this paper, we use 1 day’s prior index information to predict today’s value and repeat this over a period of time. We ignore for example stationarity considerations and extending the input window/output horizon in our analysis, as these will be discussed in future papers. The paper explains the methodology used in our analysis, gives details of general underlying background information to the architecture models (CNNs, LSTMs, GRUs and XGBoost), as well as background to regularisation techniques specifically L2 regularisation, loss curves and hyperparameter optimisation, in particular, the open-source library Optuna.

Solvency II requires that firms with Internal Models derive the Solvency Capital Requirement directly from the probability distribution forecast generated by the Internal Model. A number of UK insurance undertakings do this via an aggregation model consisting of proxy models and a copula. Since 2016 there have been a number of industry surveys on the application of these models, with the 2019 Prudential Regulation Authority (“PRA”) led industry wide thematic review identifying a number of areas of enhancement. This concluded that there was currently no uniform best practice. While there have been many competing priorities for insurers since 2019, the Working Party expects that firms will have either already made changes to their proxy modelling approach in light of the PRA survey, or will have plans to do so in the coming years. This paper takes the PRA feedback into account and explores potential approaches to calibration and validation, taking into consideration the different heavy models used within the industry and relative materiality of business lines.

Operational Risk is one of the most difficult risks to model. It is a large and diverse category covering anything from cyber losses to mis-selling fines; and from processing errors to HR issues. Data is usually lacking, particularly for low frequency, high impact losses, and consequently there can be a heavy reliance on expert judgement. This paper seeks to help actuaries and other risk professionals tasked with the challenge of validating models of operational risks. It covers the loss distribution and scenario-based approaches most commonly used to model operational risks, as well as Bayesian Networks. It aims to give a comprehensive yet practical guide to how one may validate each of these and provide assurance that the model is appropriate for a firm’s operational risk profile.