The goal of the Paris Agreement is to prevent global temperatures from rising by more than 2°C above pre-industrial levels and pursue efforts to limit them to 1.5°C above pre-industrial levels. This requires a significant reduction in global greenhouse gas emissions and achieving net zero emissions by 2050. Portfolio alignment metrics are forward-looking metrics intended to help investors understand whether their investment portfolios are on track to meet the Paris Agreement goals. They also aim to encourage capital flows towards activities needed for a net zero transition. Since 2020, several metrics have been put forward by industry groups and explored in technical papers. Companies and actuaries have been exploring the practicalities of these metrics and starting to incorporate them into investment reporting and design. But this has not been without key challenges. The Net Zero and Implications for Investment Portfolios working party aims to help actuaries improve their understanding of what net zero means for an investment portfolio and what the key mechanisms are to achieve this, as well as key challenges to date and the outlook for development.

In this paper we propose a refracted skew Brownian motion as a risk model with endogenous regime switching, which generalizes the refracted diffusion risk process introduced by Gerber and Shiu. We consider an optimal dividend problem for the refracted skew Brownian risk model and identify sufficient conditions, respectively, for barrier strategy, band strategy, and their variants to be optimal.

Extropy-based divergence measures offer distinct advantages over entropy-based counterparts, owing to their mathematical simplicity and enhanced interpretability. Relative extropy by Lad et al. [5] is a symmetric divergence measure between two probability distributions, and Mohammadi et al. [8] introduced the asymmetric divergence between two distributions based on extropy. We further study these measures, their properties, and interrelationships in this article. To address the divergence between truncated lifetime distributions, we define dynamic relative extropy for residual and past lifetime scenarios. Exploring the interrelationships of dynamic cases of relative extropy, extropy divergence, and extropy inaccuracy, we derive some unique properties and characterizations for the exponential distribution. A nonparametric estimator for relative extropy is developed, and its performance is assessed through numerical simulation studies. The practical applicability of relative extropy is used to analyze the divergence in lifetime patterns of mice under a lifetime feeding experiment and the shopping patterns of customers based on age and income groups. Further, the application of relative extropy is also applied to find the dissimilarity between two images.

Past research has indicated that the covariance of the stochastic gradient descent (SGD) error done via minibatching plays a critical role in determining its regularization and escape from low potential points. Motivated by some new research in this area, we prove universality results by showing that noise classes that have the same mean and covariance structure of SGD via minibatching have similar properties. We mainly consider the SGD algorithm, with multiplicative noise, introduced in previous work (Wu et al (2016) Int. Conf. on Machine Learning, PMLR, pp. 10367–10376), which has a much more general noise class than the SGD algorithm done via minibatching. We establish non-asymptotic bounds for the multiplicative SGD algorithm in the Wasserstein distance. We also show that the error term for the algorithm is approximately a scaled Gaussian distribution with mean 0 at any fixed point.

We consider the asymptotic behaviour of the expectation of the perimeter deviation of a uniform random spherical disc–polygon in a spherical spindle convex disc with smooth boundary. We also introduce the notion of duality on the sphere, define a model of random circumscribed disc–polygons, and determine some asymptotic results about them.

Consecutive $k$-type systems have become important in both reliability theory and applications; in spite of a large literature existing on them, three-dimensional consecutive $k$-type systems have not yet been studied for multi-state case. In this paper, we introduce several different types of multi-state linear three-dimensional consecutive $k$-type systems for the first time, with due consideration to possible overlapping of failure blocks. The finite Markov chain imbedding approach is then used for the derivation of their reliability functions with state spaces and transition matrices provided in a novel way, and the involved computational process is illustrated through several numerical examples. Finally, some possible applications of the work and potential extensions are pointed out.

We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs N, we prove that its extinction time is of order $\ln^2 N$. Interestingly, this result is valid for a general class of mating functions. Among these are the functions describing the monogamous and polygamous behavior of couples, as well as the function reducing the bisexual branching process to the simple one.

This article studies uniform inference on a function $g(\cdot )$ and its functionals in a nonparametric panel data model with fixed effects. The nonparametric panel model relaxes restrictions on time-series behavior by allowing for arbitrary types of stationary or nonstationary dependence (e.g., stationary mixingale, mildly stationary, or local-to-unity process). After removing the fixed effects via transformations, a sieve estimator is proposed, accompanied by Yurinskii’s coupling principle of Gaussian processes and uniform confidence bands (UCBs) that rely on the sieve score bootstrap method to test for linear functionals of $g(\cdot )$. Under the asymptotic framework of an increasing cross-sectional dimension and either a fixed or diverging time dimension, we prove that the bootstrapping Kolmogorov–Smirnov (sup-type) test has asymptotic uniform size controls. This article shows that our uniform inference procedure can be extended to the two-way fixed-effects nonparametric panel model with stationary mixingale regressors. Extensive simulations confirm that our sieve estimators and their UCBs work well in finite samples. The present article further applies the above methods to empirical settings and finds some interesting results in nonlinear patterns of consumption concerning income shocks and asset holdings.

In this paper, we study the self-normalized Cramér-type moderate deviation of the empirical measure of the stochastic gradient Langevin dynamics (SGLD). Consequently, we also derive the Berry–Esseen bound for the SGLD. Our approach is by constructing a stochastic differential equation to approximate the SGLD and then applying Stein’s method to decompose the empirical measure into a martingale difference series sum and a negligible remainder term.

The COVID-19 pandemic and associated non-pharmaceutical interventions (NPIs) reduced transmission of other infections. We quantified changes in hospital admission rates for respiratory and gastrointestinal infections among young children in England during and after implementation of NPIs, compared to pre-pandemic, and variations by sociodemographic and clinical characteristics. Children aged <5 years at any time between 1 January 2017 and 31 January 2022 were followed from birth or 1 January 2017, until their 5th birthday, death, or 31 January 2022, within a birth cohort based on Hospital Episode Statistics data. Quarterly emergency admission rates for respiratory and gastrointestinal infections from April-June 2020 onwards were compared to corresponding quarters in 2017–2019 using Poisson regression, with and without interaction terms for time period and sociodemographic/clinical characteristics. Admission rates for respiratory and gastrointestinal infections were lower in April–June 2020 compared to this quarter pre-pandemic (incidence rate ratio (99% CI) 0.17 (0.17–0.18) for respiratory; 0.29 (0.28–0.31) for gastrointestinal). Rates remained below pre-pandemic levels until April–June 2021 (respiratory infections) and July–September 2021 (gastrointestinal infections), subsequently increasing above the corresponding pre-pandemic quarters. Changes in rates did not differ by sociodemographic/clinical characteristics. These results can inform planning for future pandemics and their aftermath.

Antimicrobial resistance (AMR) is a pressing global health challenge, with sub-Saharan Africa experiencing the highest burden of AMR-related deaths. Inappropriate prescribing and rising antibiotic consumption drive AMR, while limited local data hampers antimicrobial stewardship efforts. This study analysed Global Point Prevalence Survey of Antimicrobial Consumption and Resistance (Global-PPS) data from Tygerberg Hospital to identify antimicrobial use trends and inform stewardship priorities. Standard Global-PPS methodology was employed at three distinct time points. All inpatients prescribed at least one antimicrobial on the day of each survey were included in the analysis. Among 3,524 hospitalized patients, 25.9% (911/3,524) received antimicrobial therapy. Overall antimicrobial use decreased significantly (p < 0.05), with the largest reduction among paediatric patients (p < 0.01). Community-acquired infections accounted for the majority of prescriptions (50.7%; 483/952) and empirical antibiotic use was high (85.3%, 872/1022). ‘Access’ antibiotics constituted 62.7% (750/1196) of prescriptions. Single-dose prescriptions for surgical prophylaxis accounted for 17.6% (15/85). This study demonstrates progress in stewardship, particularly among paediatric inpatients. Ongoing monitoring of broad-spectrum antibiotic use and adherence to single-dose surgical prophylaxis guidelines are essential priorities. Continued Global-PPS surveillance is crucial to track trends and guide future AMS interventions.

Building energy management (BEM) tasks require processing and learning from a variety of time-series data. Existing solutions rely on bespoke task- and data-specific models to perform these tasks, limiting their broader applicability. Inspired by the transformative success of Large Language Models (LLMs), Time-Series Foundation Models (TSFMs), trained on diverse datasets, have the potential to change this. Were TSFMs to achieve a level of generalizability across tasks and contexts akin to LLMs, they could fundamentally address the scalability challenges pervasive in BEM. To understand where they stand today, we evaluate TSFMs across four dimensions: (1) generalizability in zero-shot univariate forecasting, (2) forecasting with covariates for thermal behavior modeling, (3) zero-shot representation learning for classification tasks, and (4) robustness to performance metrics and varying operational conditions. Our results reveal that TSFMs exhibit limited generalizability, performing only marginally better than statistical models on unseen datasets and modalities for univariate forecasting. Similarly, inclusion of covariates in TSFMs does not yield performance improvements, and their performance remains inferior to conventional models that utilize covariates. While TSFMs generate effective zero-shot representations for downstream classification tasks, they may remain inferior to statistical models in forecasting when statistical models perform test-time fitting. Moreover, TSFMs’ forecasting performance is sensitive to evaluation metrics, and they struggle in more complex building environments compared to statistical models. These findings underscore the need for targeted advancements in TSFM design, particularly their handling of covariates and incorporating context and temporal dynamics into prediction mechanisms, to develop more adaptable and scalable solutions for BEM.

Autochthonous transmission of dengue in southern Europe has emerged as a growing public health concern, especially in regions such as Spain, due to the expansion of mosquito vector species, such as Aedes albopictus and Aedes aegypti, introduced into these regions. This article presents an overview of the situation based on the analysis of the different reports published by international and national health agencies, together with key scientific studies on autochthonous transmission of dengue in Europe and Spain. Through this work, the factors considered to be contributing or hypothesized drivers of the spread of the virus on the European continent, such as climate change, human mobility, and the proliferation of mosquito vectors, are described. It explores the cases of autochthonous transmission documented in several European countries and Spain. In addition, the surveillance protocols implemented by Spanish health authorities and the health responses to outbreaks in Spain are also examined. Finally, the risk of future transmission in Spain is assessed, and strategies are proposed to strengthen epidemiological surveillance, improve preparedness for possible outbreaks, and optimize vector-control policies in the context of global change.

Gaussian Process (GP) modeling is a probabilistic, non-parametric framework for describing spatio-temporal dependence that is well-suited for fitting risk-related surfaces. I summarize the main emerging actuarial use cases of GPs, including their applications in longevity modeling, insurance contract valuation, and loss development. The editorial also discusses further contexts with potential for GP-based approaches.

Consider a random walk in a time-inhomogeneous random environment. When the environment is stationary and ergodic, we identify a quenched harmonic function for almost every realization of the environment. This function allows us to define a random walk in a random environment conditioned to stay positive, using Doob’s h-transform.

In high-dimensional (HD) sparse linear regression, parameter selection and estimation are addressed using a constraint $l_0$ on the direction of the parameter vector. We begin by establishing a general result that identifies this direction through the leading generalized eigenspace of specific measurable matrices. Using this result, we propose a novel approach to the selection of the best subsets by solving an empirical generalized eigenvalue problem to estimate the direction of the HD parameter. We then introduce a new estimator based on the RIFLE algorithm, providing a non-asymptotic bound for the estimation risk, minimax convergence, and a central limit theorem. Simulations demonstrate the superiority of our method over existing $l_0$-constrained estimators.