We extend the classical setting of an optimal stopping problem under full information to include problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, standard filtering theory can be employed to embed the problem in a Markovian framework with one additional state variable representing the posterior of the unknown state. We provide a convenient formulation of this Markovian problem, based on a measure change technique that decouples the underlying process from the new state variable. Moreover, we show by means of several novel examples that this reduced formulation can be used to solve problems explicitly.

We propose a modification to the random destruction of graphs: given a finite network with a distinguished set of sources and targets, remove (cut) vertices at random, discarding components that do not contain a source node. We investigate the number of cuts required until all targets are removed, and the size of the remaining graph. This model interpolates between the random cutting model going back to Meir and Moon (J. Austral. Math. Soc. 11, 1970) and site percolation. We prove several general results, including that the size of the remaining graph is a tight family of random variables for compatible sequences of expander-type graphs, and determine limiting distributions for binary caterpillar trees and complete binary trees.

We consider parallel single-server queues in heavy traffic with randomly split Hawkes arrival processes. The service times are assumed to be independent and identically distributed (i.i.d.) in each queue and are independent in different queues. In the critically loaded regime at each queue, it is shown that the diffusion-scaled queueing and workload processes converge to a multidimensional reflected Brownian motion in the non-negative orthant with orthonormal reflections. For the model with abandonment, we also show that the corresponding limit is a multidimensional reflected Ornstein–Uhlenbeck diffusion in the non-negative orthant.

The current study aimed to explore Palestinian university students’ perceptions and concerns about COVID-19 vaccination hesitancy. Our sample comprised 50 university students selected using snowball sampling techniques from Palestinian universities in the West Bank, Palestine. Thematic content analysis was conducted to identify the main themes of semi-structured interviews with students. The results of the thematic content analysis yielded four main themes: Students’ perceptions and concerns on COVID-19 vaccinations, perceived risks of vaccination, experiences related to vaccination, and causes of vaccination hesitancy. Participants expressed concerns and doubts about the vaccine’s safety, showing high hesitancy and scepticism; they also reported different causes for COVID-19 vaccination hesitancy in the Palestinian context, such as the lack of confidence in vaccines, false beliefs about vaccines, and peculiar political instability and conflict of the Palestinian territories enduring a military occupation undermining the health system’s capacity to respond to the COVID-19 outbreak appropriately. Health authorities and policymakers are urgently called to invest in and potentiate awareness campaigns to change the diffuse people’s stereotypes related to the COVID-19 vaccine in the Palestinian territories.

A bootstrap percolation process on a graph with n vertices is an ‘infection’ process evolving in rounds. Let $r \ge 2$ be fixed. Initially, there is a subset of infected vertices. In each subsequent round, every uninfected vertex that has at least r infected neighbors becomes infected as well and remains so forever.

We consider this process in the case where the underlying graph is an inhomogeneous random graph whose kernel is of rank one. Assuming that initially every vertex is infected independently with probability $p \in (0,1]$, we provide a law of large numbers for the size of the set of vertices that are infected by the end of the process. Moreover, we investigate the case $p = p(n) = o(1)$, and we focus on the important case of inhomogeneous random graphs exhibiting a power-law degree distribution with exponent $\beta \in (2,3)$. The first two authors have shown in this setting the existence of a critical $p_c =o(1)$ such that, with high probability, if $p =o(p_c)$, then the process does not evolve at all, whereas if $p = \omega(p_c)$, then the final set of infected vertices has size $\Omega(n)$. In this work we determine the asymptotic fraction of vertices that will eventually be infected and show that it also satisfies a law of large numbers.

Stationary Poisson processes of lines in the plane are studied, whose directional distributions are concentrated on $k\geq 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently, the probability that the typical cell is a triangle. As a by-product, a new deviation of Miles’s classical result for the isotropic case is obtained by an approximation argument.

We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al. (2022), we consider an urban environment, represented by line segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device. Inspired by wireless network architectures, the network is additionally equipped with a second class of agents able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to chase–escape dynamics. We give conditions for parameter configurations that guarantee existence and absence of global survival as well as an in-and-out of the survival regime, depending on the speed of the devices. We also provide complementary results for the setting in which the chase–escape dynamics is defined as an independent process on the connectivity graph. The proofs mainly rest on percolation arguments via discretization and multiscale analysis.

Laboratory-based case confirmation is an integral part of measles surveillance programmes; however, logistical constraints can delay response. Use of RDTs during initial patient contact could enhance surveillance by real-time case confirmation and accelerating public health response. Here, we evaluate performance of a novel measles IgM RDT and assess accuracy of visual interpretation using a representative collection of 125 sera from the Brazilian measles surveillance programme. RDT results were interpreted visually by a panel of six independent observers, the consensus of three observers and by relative reflectance measurements using an ESEQuant Reader. Compared to the Siemens anti-measles IgM EIA, sensitivity and specificity of the RDT were 94.9% (74/78, 87.4–98.6%) and 95.7% (45/47, 85.5-99.5%) for consensus visual results, and 93.6% (73/78, 85.7–97.9%) and 95.7% (45/47, 85.5-99.5%), for ESEQuant measurement, respectively. Observer agreement, determined by comparison between individuals and visual consensus results, and between individuals and ESEQuant measurements, achieved average kappa scores of 0.97 and 0.93 respectively. The RDT has the sensitivity and specificity required of a field-based test for measles diagnosis, and high kappa scores indicate this can be accomplished accurately by visual interpretation alone. Detailed studies are needed to establish its role within the global measles control programme.

In this paper we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an application of the duality, we treat utility-based hedging in the Bachelier model. For European contingent claims with a quadratic payoff, we compute the optimal trading strategy explicitly.

Given the assumption that weather risks affect crop yields, we designed a weather index insurance product for soybean producers in the US state of Illinois. By separating the entire vegetation cycle into four growth stages, we investigate whether the phase-division procedure contributes to weather–yield loss relation estimation and, hence, to basis risk mitigation. Concretely, supposing stage-variant interaction patterns between temperature-based weather index growing degree days and rainfall-based weather index cumulative rainfall, a nonparametric weather–yield loss relation is estimated by a generalized additive model. The model includes penalized B-spline (P-spline) approach based on nonlinear optimal indemnity solutions under the expected utility framework. The P-spline analysis of variance (PS-ANOVA) method is used for efficient estimation through mixed model re-parameterization. The results indicate that the phase-division models significantly outperform the benchmark whole-cycle ones either under quadratic utility or exponential utility, given different levels of risk aversions. Finally, regarding hedging effectiveness, the expected utility ratio between the phase-division contract and the whole-cycle contract, and the percentage changes of mean root square loss and variance of revenues support the proposed phase-division contract.

This study investigates the identification and inference of quantile treatment effects (QTEs) in a fuzzy regression discontinuity (RD) design under rank similarity. Unlike Frandsen et al. (2012, Journal of Econometrics 168, 382–395), who focus on QTEs only for the compliant subpopulation, our approach can identify QTEs and average treatment effect for the whole population at the threshold. We derived a new set of moment restrictions for the RD model by imposing a local rank similarity condition, which restricts the evolution of individual ranks across treatment status in a neighborhood around the threshold. Based on the moment restrictions, we derive closed-form solutions for the estimands of the potential outcome cumulative distribution functions for the whole population. We demonstrate the functional central limit theorems and bootstrap validity results for the QTE estimators by explicitly accounting for observed covariates. In particular, we develop a multiplier bootstrap-based inference method with robustness against large bandwidths that applies to uniform inference by extending the recent work of Chiang et al. (2019, Journal of Econometrics 211, 589–618). We also propose a test for the local rank similarity assumption. To illustrate the estimation approach and its properties, we provide a simulation study and estimate the impacts of India’s 40-billion-dollar national rural road construction program on the reallocation of labor out of agriculture.

This study aims to estimate the prevalence of HIV among each of the three key populations in Vietnam: people who inject drugs (PWID), female sex workers (FSW), and men who have sex with men (MSM) and quantify their shared risk factors for HIV infection through a systematic review and meta-analysis of recent literature (published in 2001–2017) in the relevant topics. A total of 17 studies consisting of 16,304 participants were selected in this review. The meta-analysis results revealed that the pooled prevalence estimates with 95% confidence intervals (CIs) among PWID, FSW, and MSM were: 0.293 (0.164, 0.421), 0.075 (0.060, 0.089), and 0.085 (0.044, 0.126), respectively. The findings also indicated that injecting drug use (OR: 9.88, 95%CI: 4.47–15.28), multiperson use of injecting equipment (OR: 2.91, 95%CI: 1.69, 4.17), and inconsistent condom use (OR: 2.11, 95%CI: 1.33, 2.90) were the shared risk factors for HIV infection among these population groups. The findings highlighted the importance of HIV prevention approaches to addressing the shared sexual and drug-related practices among the key populations in consideration of their overlapping social networks.

Omega ratio, a risk-return performance measure, is defined as the ratio of the expected upside deviation of return to the expected downside deviation of return from a predetermined threshold described by an investor. Motivated by finding a solution protected against sampling errors, in this paper, we focus on the worst-case Omega ratio under distributional uncertainty and its application to robust portfolio selection. The main idea is to deal with optimization problems with all uncertain parameters within an uncertainty set. The uncertainty set of the distribution of returns given characteristic information, including the first two orders of moments and the Wasserstein distance, can handle data problems with uncertainty while making the calculation feasible.