The protection number of a vertex $v$ in a tree is the length of the shortest path from $v$ to any leaf contained in the maximal subtree where $v$ is the root. In this paper, we determine the distribution of the maximum protection number of a vertex in simply generated trees, thereby refining a recent result of Devroye, Goh, and Zhao. Two different cases can be observed: if the given family of trees allows vertices of outdegree $1$, then the maximum protection number is on average logarithmic in the tree size, with a discrete double-exponential limiting distribution. If no such vertices are allowed, the maximum protection number is doubly logarithmic in the tree size and concentrated on at most two values. These results are obtained by studying the singular behaviour of the generating functions of trees with bounded protection number. While a general distributional result by Prodinger and Wagner can be used in the first case, we prove a variant of that result in the second case.

High-cardinality categorical features are pervasive in actuarial data (e.g., occupation in commercial property insurance). Standard categorical encoding methods like one-hot encoding are inadequate in these settings.

In this work, we present a novel Generalised Linear Mixed Model Neural Network (“GLMMNet”) approach to the modelling of high-cardinality categorical features. The GLMMNet integrates a generalised linear mixed model in a deep learning framework, offering the predictive power of neural networks and the transparency of random effects estimates, the latter of which cannot be obtained from the entity embedding models. Further, its flexibility to deal with any distribution in the exponential dispersion (ED) family makes it widely applicable to many actuarial contexts and beyond. In order to facilitate the application of GLMMNet to large datasets, we use variational inference to estimate its parameters—both traditional mean field and versions utilising textual information underlying the high-cardinality categorical features.

We illustrate and compare the GLMMNet against existing approaches in a range of simulation experiments as well as in a real-life insurance case study. A notable feature for both our simulation experiment and the real-life case study is a comparatively low signal-to-noise ratio, which is a feature common in actuarial applications. We find that the GLMMNet often outperforms or at least performs comparably with an entity-embedded neural network in these settings, while providing the additional benefit of transparency, which is particularly valuable in practical applications.

Importantly, while our model was motivated by actuarial applications, it can have wider applicability. The GLMMNet would suit any applications that involve high-cardinality categorical variables and where the response cannot be sufficiently modelled by a Gaussian distribution, especially where the inherent noisiness of the data is relatively high.

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.

The Internet of Things (IoT) and wearable computing are crucial elements of modern information systems and applications in which advanced features for user interactivity and monitoring are required. However, in the fields of pervasive gaming, IoT has had limited real-world applications. In this work, we present a prototype of a wearable platform for pervasive games that combines IoT with wearable computing to enable the real-time monitoring of physical activity. The main objective of the solution is to promote the utilization of gamification techniques to enhance the physical activity of users through challenges and quests. This aims to create a symbolic link between the virtual gameplay and the real-world environment without the requirement of a smartphone. With the integration of sensors and wearable devices by design, the platform has the capability of real-time monitoring the users’ physical activity during the game. The system performance results highlight the efficiency and attractiveness of the wearable platform for gamifying physical activity.

Compressible anisothermal flows, which are commonly found in industrial settings such as combustion chambers and heat exchangers, are characterized by significant variations in density, viscosity, and heat conductivity with temperature. These variations lead to a strong interaction between the temperature and velocity fields that impacts the near-wall profiles of both quantities. Wall-modeled large-eddy simulations (LESs) rely on a wall model to provide a boundary condition, for example, the shear stress and the heat flux that accurately represents this interaction despite the use of coarse cells near the wall, and thereby achieve a good balance between computational cost and accuracy. In this article, the use of graph neural networks for wall modeling in LES is assessed for compressible anisothermal flow. Graph neural networks are a type of machine learning model that can learn from data and operate directly on complex unstructured meshes. Previous work has shown the effectiveness of graph neural network wall modeling for isothermal incompressible flows. This article develops the graph neural network architecture and training to extend their applicability to compressible anisothermal flows. The model is trained and tested a priori using a database of both incompressible isothermal and compressible anisothermal flows. The model is finally tested a posteriori for the wall-modeled LES of a channel flow and a turbine blade, both of which were not seen during training.

This paper examines the potential role of network analysis in understanding the powerful elites that pose a significant threat to peace and state-building within post-conflict contexts. This paper makes a threefold contribution. First, it identifies a caveat in the scholarship surrounding international interventions, shedding light on shortcomings in their design and implementation strategies, and elucidating the influence these elites wield in the political and economic realms. Next, it delineates the essentials of the network analysis approach, addressing the information and data requirements and limitations inherent in its application in conflict environments. Finally, the paper provides valuable insights gleaned from the international operation in Guatemala known as the International Commission for Impunity in Guatemala, which specifically targeted illicit networks. The argument asserts that network analysis functions as a dual-purpose tool—serving as both a descriptive instrument to reveal, identify, and address the root causes of conflict and a predictive tool to enhance peace agreement implementation and improve decision-making. Simultaneously, it underscores the challenge of data analysis and translating network interventions into tangible real-life consequences for long-lasting results.

We introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

A version of the classical Buffon problem in the plane naturally extends to the setting of any Riemannian surface with constant Gaussian curvature. The Buffon probability determines a Buffon deficit. The relationship between Gaussian curvature and the Buffon deficit is similar to the relationship that the Bertrand–Diguet–Puiseux theorem establishes between Gaussian curvature and both circumference and area deficits.

Previous studies suggest that influenza virus infection may provide temporary non-specific immunity and hence lower the risk of non-influenza respiratory virus infection. In a randomized controlled trial of influenza vaccination, 1 330 children were followed-up in 2009–2011. Respiratory swabs were collected when they reported acute respiratory illness and tested against influenza and other respiratory viruses. We used Poisson regression to compare the incidence of non-influenza respiratory virus infection before and after influenza virus infection. Based on 52 children with influenza B virus infection, the incidence rate ratio (IRR) of non-influenza respiratory virus infection after influenza virus infection was 0.47 (95% confidence interval: 0.27–0.82) compared with before infection. Simulation suggested that this IRR was 0.87 if the temporary protection did not exist. We identified a decreased risk of non-influenza respiratory virus infection after influenza B virus infection in children. Further investigation is needed to determine if this decreased risk could be attributed to temporary non-specific immunity acquired from influenza virus infection.

We give algorithms for approximating the partition function of the ferromagnetic $q$-color Potts model on graphs of maximum degree $d$. Our primary contribution is a fully polynomial-time approximation scheme for $d$-regular graphs with an expansion condition at low temperatures (that is, bounded away from the order-disorder threshold). The expansion condition is much weaker than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models; we use extremal graph theory and applications of Karger’s algorithm to count cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We also obtain efficient algorithms in the Gibbs uniqueness region for bounded-degree graphs. While our high-temperature proof follows more standard polymer model analysis, our result holds in the largest-known range of parameters $d$ and $q$.

We consider the super-replication problem for a class of exotic options known as life-contingent options within the framework of the Black–Scholes market model. The option is allowed to be exercised if the death of the option holder occurs before the expiry date, otherwise there is a compensation payoff at the expiry date. We show that there exists a minimal super-replication portfolio and determine the associated initial investment. We then give a characterisation of when replication of the option is possible. Finally, we give an example of an explicit super-replicating hedge for a simple life-contingent option.

Let $\mathcal{C}$ denote the family of all coherent distributions on the unit square $[0,1]^2$, i.e. all those probability measures $\mu$ for which there exists a random vector $(X,Y)\sim \mu$, a pair $(\mathcal{G},\mathcal{H})$ of $\sigma$-fields, and an event E such that $X=\mathbb{P}(E\mid\mathcal{G})$, $Y=\mathbb{P}(E\mid\mathcal{H})$ almost surely. We examine the set $\mathrm{ext}(\mathcal{C})$ of extreme points of $\mathcal{C}$ and provide its general characterisation. Moreover, we establish several structural properties of finitely-supported elements of $\mathrm{ext}(\mathcal{C})$. We apply these results to obtain the asymptotic sharp bound $\lim_{\alpha \to \infty}\alpha\cdot(\sup_{(X,Y)\in \mathcal{C}}\mathbb{E}|X-Y|^{\alpha}) = {2}/{\mathrm{e}}$.

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.

Expectiles have received increasing attention as a risk measure in risk management because of their coherency and elicitability at the level $\alpha\geq1/2$. With a view to practical risk assessments, this paper delves into the worst-case expectile, where only partial information on the underlying distribution is available and there is no closed-form representation. We explore the asymptotic behavior of the worst-case expectile on two specified ambiguity sets: one is through the Wasserstein distance from a reference distribution and transforms this problem into a convex optimization problem via the well-known Kusuoka representation, and the other is induced by higher moment constraints. We obtain precise results in some special cases; nevertheless, there are no unified closed-form solutions. We aim to fully characterize the extreme behaviors; that is, we pursue an approximate solution as the level $\alpha $ tends to 1, which is aesthetically pleasing. As an application of our technique, we investigate the ambiguity set induced by higher moment conditions. Finally, we compare our worst-case expectile approach with a more conservative method based on stochastic order, which is referred to as ‘model aggregation’.

We show joint convergence of the Łukasiewicz path and height process for slightly supercritical Galton–Watson forests. This shows that the height processes for supercritical continuous-state branching processes as constructed by Lambert (2002) are the limit under rescaling of their discrete counterparts. Unlike for (sub-)critical Galton–Watson forests, the height process does not encode the entire metric structure of a supercritical Galton–Watson forest. We demonstrate that this result is nonetheless useful, by applying it to the configuration model with an independent and identically distributed power-law degree sequence in the critical window, of which we obtain the metric space scaling limit in the product Gromov–Hausdorff–Prokhorov topology, which is of independent interest.

In this paper we extend results on reconstruction of probabilistic supports of independent and identically distributed random variables to supports of dependent stationary ${\mathbb R}^d$-valued random variables. All supports are assumed to be compact of positive reach in Euclidean space. Our main results involve the study of the convergence in the Hausdorff sense of a cloud of stationary dependent random vectors to their common support. A novel topological reconstruction result is stated, and a number of illustrative examples are presented. The example of the Möbius Markov chain on the circle is treated at the end with simulations.

This paper presents an asymptotic theory for recurrent jump diffusion models with well-defined scale functions. The class of such models is broad, including general nonstationary as well as stationary jump diffusions with state-dependent jump sizes and intensities. The asymptotics for recurrent jump diffusion models with scale functions are largely comparable to the asymptotics for the corresponding diffusion models without jumps. For stationary jump diffusions, our asymptotics yield the usual law of large numbers and the standard central limit theory with normal limit distributions. The asymptotics for nonstationary jump diffusions, on the other hand, are nonstandard and the limit distributions are given as generalized diffusion processes.

Precision healthcare is an emerging field of science that utilizes an individual’s health information, context, and genetics to provide more personalized diagnostics and treatments. In this manuscript, we leverage that concept and present a group of machine learning models for precision gaming. These predictive models guide adolescents through best practices related to their health. The use case deployed is for girls in India through a mobile application released in three different Indian states. To evaluate the usability of the models, experiments are designed and data (demographic, behavioral, and health-related) are collected. The experimental results are presented and discussed.

Hand hygiene (HH) is the paramount measure used to prevent healthcare-associated infections. A repeated cross-sectional study was undertaken with direct observation of the degree of compliance on HH of healthcare personnel during the SARS-CoV-2 pandemic. Between, 2018–2019, 9,083 HH opportunities were considered, and 5,821 in 2020–2022. Chi squared tests were used to identify associations. The crude and adjusted odds ratios were used along with a logistic regression model for statistical analyses. Compliance on HH increased significantly (p < 0.001) from 54.5% (95% CI: 53.5, 55.5) to 70.1% (95% CI: 68.9, 71.2) during the COVID-19 pandemic. This increase was observed in four of the five key moments of HH established by the World Health Organization (WHO) (p < 0.05), except at moment 4. The factors that were significantly and independently associated with compliance were the time period considered, type of healthcare-personnel, attendance at training sessions, knowledge of HH and WHO guidelines, and availability of hand disinfectant alcoholic solution in pocket format. Highest HH compliance occurred during the COVID-19 pandemic, reflecting a positive change in healthcare-personnel’s behaviour regarding HH recommendations.

We consider local level and local linear estimators for estimation and inference in time-varying parameter (TVP) regressions with general stationary covariates. The latter estimator also yields estimates for parameter derivatives that are utilized for the development of time invariance tests for the regression coefficients. Our theoretical framework is general enough to allow for a wide range of stationary regressors, including stationary long memory. We demonstrate that neglecting time variation in the regression parameters has a range of adverse effects in inference, in particular, when regressors exhibit long-range dependence. For instance, parametric tests diverge under the null hypothesis when the memory order is strictly positive. The finite sample performance of the methods developed is investigated with the aid of a simulation experiment. The proposed methods are employed for exploring the predictability of SP500 returns by realized variance. We find evidence of time variability in the intercept as well as episodic predictability when realized variance is utilized as a predictor in TVP specifications.