We introduce the concept of arbitrable stochastic games, which appears to be new. To do so, we consider a reward criterion different from the standard gamma-weighted criterion. This allows us to define the fair price to play a non-competitive stochastic game. We then illustrate the concept through three variations of the classical coin-toss game with chips, providing proofs via Doob’s theorem for supermartingales and practical algorithms. These examples deepen our understanding of the Bitcoin protocol.

Indonesia’s rapid digital transformation generates massive economic opportunities while posing new regulatory challenges. This study examines how Indonesia’s digital economy is governed through key regulatory domains: electronic commerce, data governance, and digital taxation, and assesses their impact on inclusive growth. The research utilizes an integrated theoretical lens, Institutional Theory and Digital Divide Theory, to analyze how formal rules and on-the-ground access to technology together shape outcomes. The research employs a multimethod approach, to understand how different regulatory models influence market participation, business compliance, and digital inclusion. The findings reveal significant regional disparities in internet access and digital business adoption, with rural and remote areas lagging behind urban centers. Micro, small, and medium-sized enterprises face disproportionate compliance burdens under current regulations, a gap partly addressed through cooperative initiatives like the Indonesia–Japan Track 1.5 Public–Private Partnership. A key insight is the complex impact of data localization policies: while strengthening digital sovereignty and user privacy, strict localization requirements can raise operational costs and deter foreign investment. The paper concludes with policy recommendations for improving regulatory implementation, expanding digital infrastructure and literacy, and fostering international cooperation to ensure Indonesia’s digital economy regulations promote equitable growth across its diverse archipelago.

Evidence on the association between chronic hepatitis B virus (HBV) infection and stroke is limited, inconsistent, and confined predominantly to endemic regions in Asia. This study investigated the association between chronic HBV infection and stroke using data from the largest healthcare provider in Israel. All individuals aged 20 and older who were tested for hepatitis B surface antigen (HBsAg) between 2005 and 2023 were identified. Newly diagnosed HBV patients (HBsAg-positive) were propensity scorematched to non-HBV subjects (HBsAg-negative) in a 1:4 ratio and followed for stroke occurrence through 2024. The study included 20 544 HBV patients and 82 176 matched controls. Overall stroke was diagnosed in 472 HBV patients and 1 717 controls (incidence rates: 2.13 vs. 1.94 per 1 000 person-years). Hazard ratios were 1.09 (95% CI, 0.98–1.22) for overall stroke, 1.01 (0.89–1.14) for ischemic stroke, and 1.82 (1.35–2.45) for intracerebral hemorrhage (ICH). Ischemic stroke risk was specifically increased in younger individuals and females (p-for-interaction = 0.006 and 0.079, respectively). Results remained consistent when excluding patients with prior stroke. Exploratory analysis suggested hepatitis D coinfection is associated with increased ICH risk. In conclusion, chronic HBV infection was associated with significantly increased ICH risk, with subgroup-specific increases in ischemic stroke risk.

This paper pays attention to the frequency polygon, which is constructed by connecting with straight lines the mid-bin values of a histogram. As a density estimator based on the histogram technique, the frequency polygon has the advantage of computational simplicity and has been widely used in many fields. The purpose of this article is to investigate the weak consistency, the uniformly weak consistency, and the rate of the uniformly weak consistency for frequency polygon estimation of the density function under $\alpha$-mixing samples, which improve and extend the corresponding ones in the literature. In addition, the simulation study and real data analysis are also presented to verify the validity of the theoretical results based on finite samples.

This paper assesses the impact of demographic risk on a portfolio of equity-linked insurance contracts featuring a Cliquet-style guarantee, in which the policyholder accrues, on an annual basis, interest equal to the maximum between the return on a risky portfolio and a guaranteed minimum rate. We provide closed-form expressions for inflows, outflows, and reserves for such a portfolio through a cohort-based approach. In accordance with market-consistent actuarial principles, we determine both the no-arbitrage value of the liabilities and the structure of the hedging portfolio that replicates the guaranteed benefits. We quantify demographic risk by separately assessing the capital requirements for both idiosyncratic and trend risks. The capital requirement is computed over a one-year horizon using a 99.5% Value-at-Risk measure, consistent with the Solvency II regulatory framework. The model accommodates different regulatory contexts, allowing for jurisdiction-specific rules and accounting standards. Numerical simulations highlight how the portfolio’s risk profile is affected by demographic volatility, which is influenced by policyholder age, policy duration, and dispersion of the sums insured. Additionally, trend risk depends on both mortality volatility and the specification of the longevity model. This framework supports insurers in evaluating, hedging, and managing demographic risk in market-linked life insurance products.

Fluctuations in disease severity occurred throughout the COVID-19 pandemic in England due to emerging variants and changing population immunity. Deaths caused by COVID-19 reduced from 2022; however, a smaller reduction was observed in deaths following a COVID-19 test. This study examines whether mortality risk within 28 days of a positive SARS-CoV-2 test remained elevated during a period of reduced disease severity. National-level routinely collected health data containing SARS-CoV-2 test results, vaccination, hospital, and death records were linked to create a population-level cohort. Individuals testing positive and negative were matched on demographic and disease characteristics. Mortality risk was compared using univariable and multivariable conditional logistic regression models for the overall time-period (March 2020–April 2022) and the focus time-period (January–April 2022). Individuals testing positive in the overall time-period had a 228% increased risk of death than those testing negative. In the focused time-period, test positive individuals had 63% higher odds of death, accounting for vaccination and previous hospitalisation. The increased risk of death associated with testing positive was greater among unvaccinated individuals (238%) than vaccinated individuals (155%). Mortality risk following COVID-19 remained elevated at the end of the pandemic, especially among unvaccinated individuals, supporting continued COVID-19 booster vaccination campaigns.

Non-pharmaceutical interventions (NPIs) imposed during the COVID-19 pandemic were known to create an immunity debt. This study aimed to quantify the immunity debt for respiratory syncytial virus (RSV), adenovirus, group A Streptococcus (GAS), and influenza in Japan between 2014 and 2024. We conducted a retrospective observational study using national surveillance data and electronic health records in 23 clinics. We conducted an interrupted time series analysis using a quasi-Poisson regression model to estimate the counterfactual incidence that would have occurred in the absence of NPIs. The number of RSV cases declined by 84% in the 2020–2021 season and increased by 39% in the 2021–2022 season, primarily due to an increase in cases among 2-year-old children (94%). Adenovirus, GAS, and influenza were suppressed during the 2020–2022 season by 58–99%. Adenovirus cases increased by 195% in 2023, with a 458% increase among children aged 5–9 years. GAS increased by 36% in 2024, with a 96% increase among 10- to 14-year-olds. Influenza increased by 158% in 2023, with a 299% increase among 10- to 14-year-olds. Surveillance data and 23 clinics’ data showed similar trends. The study suggests that the intensity and timing of the immunity debt differed by pathogen.

We study the local asymptotic behaviour of divergence-like functionals of a family of d-dimensional infinitely divisible random fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of fields when the region of integration shrinks to a single point. We show that in most cases, convergence stably in distribution holds after a proper normalisation. Furthermore, the limit random fields can be described in terms of stochastic integrals with respect to a Lévy basis. We additionally discuss the relationship between our results and the advective kinetic energy flux in a possibly turbulent flow.

In 2024, an outbreak of Salmonella typhimurium affected two regions in Portugal. To identify the vehicle, we conducted a case–case study using a ‘same disease, different time period’ design. We compared S. typhimurium cases linked by whole-genome sequencing (WGS) (cluster cases) with salmonellosis cases notified in 2023 (historical cases) and calculated odds ratios (OR) for food exposures in surveillance data using logistic regression. We performed WGS on 58 isolates from the outbreak period (11/03/2024–2118/06/2024), and all belonged to a single cgMLST cluster (HierCC HC5_410,410). Compared with the 552 historical cases, cluster cases more frequently reported fresh cheese consumption (OR 18; 95% CI: 8.5–38). We visited the implicated cheese production site, identified food safety non-conformities, and enforced hygiene measures. Environmental and product specimens collected at the visit tested negative for Salmonella spp. Taken together, the most plausible vehicle in this outbreak was fresh cheese. The case–case design enabled a rapid, low-cost analysis to support targeted investigation using surveillance data. Using WGS cluster cases as the case definition, rather than all S. typhimurium cases during the outbreak period, yielded a higher OR in the case–case study, increasing confidence in the findings. We recommend this combined approach as part of the toolkit for foodborne outbreak investigations in Portugal in similar contexts.

Cholera remains a major public health concern in conflict-affected Tigray, Ethiopia, where disrupted water, sanitation, and hygiene (WaSH) services and displacement have increased transmission risk. This study analysed outbreak dynamics, attack rates (AR), and predictors of cholera to inform interventions aligned with Ethiopia’s Cholera Elimination Plan (2022–2028). A retrospective analysis was conducted on 802 suspected and confirmed cholera cases reported from 25 July to 4 October 2024 across 25 districts in Central and Northwestern Tigray. Data from the Tigray Health Research Institute line list were analysed using descriptive statistics, Chi-square tests, and Generalized Estimating Equation (GEE) models. Attack rates were highest in Asgede (357.25/100000) and Endabaguna (88.12/100000). Significant associations were observed with age, sex, occupation, water source, travel history, vaccination, latrine access, and contact history. GEE analysis showed strong intra-cluster correlation (α = 0.949). Higher odds of cholera were associated with males, adults aged 16–45 years, and use of unsafe water sources, while vaccination and latrine availability reduced risk. Strengthening WaSH services, vaccination coverage, surveillance, and targeted risk communication is essential to reduce cholera transmission in Tigray.

This study aimed to identify determinants of influenza vaccination among older adults using nationally representative data from the Turkey Older Persons Profile Survey 2023. Data from 11 657 individuals aged 65 and over, collected by the Turkish Statistical Institute, were analysed. Least Absolute Shrinkage and Selection Operator regression was employed for variable selection, followed by binary logistic regression to identify significant predictors. Only 19.4% of older adults reported receiving an influenza vaccine during the 2022/2023 influenza season. Higher education, income sufficiency, social security coverage, regular medication use, physical activity, and use of mobile health (mHealth) applications were significantly associated with higher vaccination uptake. Former smoking, alcohol consumption, older age, higher body mass index, and greater independence in daily living were also positive predictors. Traditional barriers to healthcare access (e.g., transportation, waiting times) were not significantly associated. Regional disparities were evident, with lower vaccination rates in the eastern regions. Vaccine uptake among older adults in Turkey is low despite universal access. Promoting engagement with primary healthcare services and increasing the use of mHealth applications may contribute to increasing vaccination coverage. Special attention should be given to socially disadvantaged groups and underperforming regions to enhance preventive healthcare among the aging population.