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.

Turn-of-the-century America witnessed many forgotten risk-making experiments that probed the limits of insurability by stepping beyond the familiar fields of life, fire, and marine insurance. One attempted to underwrite firms’ lost profits during strikes.

The ensuing debates on strike insurance’s practicability revealed scientistic expectations of never-ending actuarial progress that united an otherwise-divided business community. Yet attempting to realize strike insurance quickly meant grappling with the limits of insurability. Labor strife’s fuzzy causality involving human agency forestalled the homogenous classification that underlay actuaries’ averaging. Thus, strike underwriters sidestepped actuarial ratemaking to offer uniform premiums to those deemed acceptable risks. This solution not only left them susceptible to adverse selection and moral hazard but also highlighted the limits of insurers’ ability to transform uncertainty into commoditized risk, more broadly.

Recognizing these limits has important historiographical implications. Based largely on studies of life insurance—the gold standard of insurability—the rise of financial risk management has claimed a central place in the history of American capitalism. This literature thus threatens to obscure the ongoing significance of unclassifiable, unquantifiable uncertainty. Uncovering forgotten risk-making projects like attempts to establish strike insurance, where Americans grappled with the limits of insurability, is thus a crucial corrective.

We use Benford's law to examine the non-random elements of health care costs. We find that as health care expenditures increase, the conformity to the expected distribution of naturally occurring numbers worsens, indicating a tendency towards inefficient treatment. Government insurers follow Benford's law better than private insurers indicating more efficient treatment. Surprisingly, self-insured patients suffer the most from non-clinical cost factors. We suggest that cost saving efforts to reduce non-clinical expenses should be focused on more severe, costly encounters. Doing so focuses cost reduction efforts on less than 10% of encounters that constitute over 70% of dollars spent on health care treatment.

Wealth provides self-insurance against financial risk, reducing risk aversion. We apply this insurance mechanism to electoral behaviour, arguing that a voter who desires a change to the status quo and who is wealthy is more likely to vote for change than a voter who lacks the same self-insurance. We apply this argument to the case of Brexit in the UK, which has been widely characterized as a vote by the ‘economically left-behind’. Our results show that individuals who lacked wealth are less likely to support leaving the EU, explaining why so many Brexit voters were wealthy, in terms of their property wealth. We corroborate our theory using two panel surveys, accounting for unobserved individual-level heterogeneity, and by using a survey experiment. The findings have implications for the potential broader role of wealth-as-insurance in electoral behaviour and for understanding the Brexit case.

Motivated by insurance applications, we propose a new approach for the validation of real-world economic scenarios. This approach is based on the statistical test developed by Chevyrev and Oberhauser ((2022) Journal of Machine Learning Research, 23(176), 1–42.) and relies on the notions of signature and maximum mean distance. This test allows to check whether two samples of stochastic processes paths come from the same distribution. Our contribution is to apply this test to a variety of stochastic processes exhibiting different pathwise properties (Hölder regularity, autocorrelation, and regime switches) and which are relevant for the modelling of stock prices and stock volatility as well as of inflation in view of actuarial applications.

Sickness insurance companies were developed in Spain by doctors and healthcare professionals, remaining outside the interests of general insurance companies. Their management was hardly professional, with limited actuarial techniques and they only accounted for a small percentage of total insurance business premiums. From the 1970s onwards, various factors changed this situation, driving processes of concentration, with numerous takeovers and mergers, first reducing the number of local and regional companies to the benefit of companies of national scope. Subsequently, the growth in demand for this type of coverage sparked the interest of national general insurance companies and multinationals, leading to a restructuring of the sector which has progressively acquired greater weight within the insurance business and become increasingly internationalised. This last stage immersed the health sector in Spain in the great processes of globalisation of the sector, characterised by a financialisation of capital promoted by the bank investment funds. These processes are little known and are the focus of analysis of this paper, with the aim of enabling comparison at international level.

Physician-based transparency approaches have been advanced as a strategy for informing patients of the likely financial consequences of using services. The structure of health care pricing and insurance coverage, and the low uptake of existing tools, suggest these approaches are likely to be unwieldy and unsuccessful. They may also generate new ethical challenges.

This paper introduces gemact, a Python package for actuarial modeling based on the collective risk model. The library supports applications to risk costing and risk transfer, loss aggregation, and loss reserving. We add new probability distributions to those available in scipy, including the (a, b, 0) and (a, b, 1) discrete distributions, copulas of the Archimedean family, the Gaussian, the Student t and the Fundamental copulas. We provide an implementation of the AEP algorithm for calculating the cumulative distribution function of the sum of dependent, nonnegative random variables, given their dependency structure specified with a copula. The theoretical framework is introduced at the beginning of each section to give the reader with a sufficient understanding of the underlying actuarial models.

The valuation of insurance liabilities has traditionally been dealt with by actuaries, who closely monitored underlying illiquid features, assumed a long-term perspective, and exercised their own subjective, expert judgment. However, the new EU regulatory regime of Solvency II (S2) has come to require market-consistent valuation supplemented by a risk-sensitive capital. This is considered an unwanted shift towards short-termism that is misaligned with the industry's long term and countercyclical character. The new principles place the ‘technicalising’ logic of financial economics over ‘contextualising’ actuarial know-how. Following existing analytics of valuation from the ethnography of reinsurance markets and the social studies of finance, such requirements appear either as an alarming attack against the actuarial component of traditional valuation practice, or else as a preserver of it, through a process of enfolding at the heart of the financialisation project. This article holds that the case of S2 challenges both these analytics of valuation. S2’s financialisation project, precisely by attempting to construct itself, deconstructs itself into an actuarial project, in a recurring, aporetic process. In this respect, fair (or otherwise) valuation remains always undecidable, inconclusive, and thus responsible.

We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.