We study an optimal investment problem under a joint limited expected relative loss and portfolio insurance constraint with a general random benchmark. By making use of a static Lagrangian method in a complete market setting, the optimal wealth and investment strategy can be fully determined along with the existence and uniqueness of the Lagrangian multipliers. Our numerical demonstration for various commonly used random benchmarks shows a trade-off between the portfolio outperformance and underperformance relative to the benchmark, which may not be captured by the widely used Omega ratio and its utility-transformed version, reflecting the impact of the benchmarking loss constraint. Furthermore, we develop a new portfolio performance measurement indicator that incorporates the agent’s utility loss aversion relative to the benchmark via solving an equivalent optimal asset allocation problem with a benchmark-reference-based preference. We show that the expected utility performance is well depicted by looking at this new portfolio performance ratio, suggesting a more suitable portfolio performance measurement under a limited loss constraint relative to a possibly random benchmark.

One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb {R}^d$ and a random direction movement scheme. Given a fixed time horizon $T>0$, we model these movements via cylinders in $\mathbb {R}^d \times [0,T]$. In this work, we derive central limit theorems for functionals of the union of these cylinders. The volume and the number of isolated cylinders and the Euler characteristic of the random set are considered and give an answer to the achievable throughput, the availability of nodes, and the topological structure of the network.

We investigated seroprevalence and factors associated with Leptospira spp. infections in humans in rural Northern Germany. Sera of 450 participants were tested for leptospira-reactive IgG antibodies by two enzyme-linked immunosorbent assays (ELISA). A narrow (specific) and a broad (sensitive) case definition were applied and results compared in the analysis. Personal data were collected via questionnaire and associations with the serostatus were investigated by multivariable logistic regression. The seroprevalence estimates were 1.6% (95%-confidence interval (CI) = 0.63–3.2) under the narrow and 4.2% (95%-CI = 2.6–6.5%) under the broad case definition. Few (14%) participants knew about the pathogen. No seropositive participant recalled a prior leptospirosis diagnosis. Spending more than two hours a week in the forest was significantly associated with anti-leptospira IgG in both models (broad case definition: adjusted odds ratio (aOR) = 2.8, 95%-CI = 1.2–9.1; narrow case definition: aOR = 11.1, 95%-CI = 1.3–97.1). Regular cleaning of storage rooms was negatively associated in the broad (aOR = 0.17, 95%-CI = 0.03–0.98) and touching a dead rodent in the past 10 years in the narrow case definition model (aOR = 0.23, 95%-CI = 0.05–1.04). Our findings support risk factors identified in previous investigations. To counter the low awareness for the pathogen, we recommend that health authorities communicate risks and preventive measures to the public by using target-group specific channels.

In this paper, we investigate the pricing of vulnerable European options in a market where the underlying stocks are not perfectly liquid. A liquidity discount factor is used to model the effect of liquidity risk in the market, and the default risk of the option issuer is incorporated into the model using a reduced-form model, where the default intensity process is correlated with the liquidity risk. We obtain a semiclosed-form pricing formula of vulnerable options through the inverse Fourier transform. Finally, we illustrate the effects of default risk and liquidity risk on option prices numerically.

Broiler chickens are among the main livestock sectors worldwide. With individual treatments being inapplicable, contrary to many other animal species, the need for antimicrobial use (AMU) is relatively high. AMU in animals is known to drive the emergence and spread of antimicrobial resistance (AMR). High farm biosecurity is a cornerstone for animal health and welfare, as well as food safety, as it protects animals from the introduction and spread of pathogens and therefore the need for AMU. The goal of this study was to identify the main biosecurity practices associated with AMU in broiler farms and to develop a statistical model that produces customised recommendations as to which biosecurity measures could be implemented on a farm to reduce its AMU, including a cost-effectiveness analysis of the recommended measures. AMU and biosecurity data were obtained cross-sectionally in 2014 from 181 broiler farms across nine European countries (Belgium, Bulgaria, Denmark, France, Germany, Italy, the Netherlands, Poland and Spain). Using mixed-effects random forest analysis (Mix-RF), recursive feature elimination was implemented to determine the biosecurity measures that best predicted AMU at the farm level. Subsequently, an algorithm was developed to generate AMU reduction scenarios based on the implementation of these measures. In the final Mix-RF model, 21 factors were present: 10 about internal biosecurity, 8 about external biosecurity and 3 about farm size and productivity, with the latter showing the largest (Gini) importance. Other AMU predictors, in order of importance, were the number of depopulation steps, compliance with a vaccination protocol for non-officially controlled diseases, and requiring visitors to check in before entering the farm. K-means clustering on the proximity matrix of the final Mix-RF model revealed that several measures interacted with each other, indicating that high AMU levels can arise for various reasons depending on the situation. The algorithm utilised the AMU predictive power of biosecurity measures while accounting also for their interactions, representing a first step toward aiding the decision-making process of veterinarians and farmers who are in need of implementing on-farm biosecurity measures to reduce their AMU.

We introduce a variant of Shepp’s classical urn problem in which the optimal stopper does not know whether sampling from the urn is done with or without replacement. By considering the problem’s continuous-time analog, we provide bounds on the value function and, in the case of a balanced urn (with an equal number of each ball type), an explicit solution is found. Surprisingly, the optimal strategy for the balanced urn is the same as in the classical urn problem. However, the expected value upon stopping is lower due to the additional uncertainty present.

In the classical framework, a random walk on a group is a Markov chain with independent and identically distributed increments. In some sense, random walks are time and space homogeneous. This paper is devoted to a class of inhomogeneous random walks on $\mathbb{Z}^d$ termed ‘Markov additive processes’ (also known as Markov random walks, random walks with internal degrees of freedom, or semi-Markov processes). In this model, the increments of the walk are still independent but their distributions are dictated by a Markov chain, termed the internal Markov chain. While this model is largely studied in the literature, most of the results involve internal Markov chains whose operator is quasi-compact. This paper extends two results for more general internal operators: a local limit theorem and a sufficient criterion for their transience. These results are thereafter applied to a new family of models of drifted random walks on the lattice $\mathbb{Z}^d$.

Higher-order networks aim at improving the classical network representation of trajectories data as memory-less order $1$ Markov models. To do so, locations are associated with different representations or “memory nodes” representing indirect dependencies between visited places as direct relations. One promising area of investigation in this context is variable-order network models as it was suggested by Xu et al. that random walk-based mining tools can be directly applied on such networks. In this paper, we focus on clustering algorithms and show that doing so leads to biases due to the number of nodes representing each location. To address them, we introduce a representation aggregation algorithm that produces smaller yet still accurate network models of the input sequences. We empirically compare the clustering found with multiple network representations of real-world mobility datasets. As our model is limited to a maximum order of $2$, we discuss further generalizations of our method to higher orders.

This study investigated Coronavirus disease 2019 (COVID-19) vaccine acceptance, and compared the potential factors influencing vaccine acceptance and hesitancy between public university (PuU) and private university (PrU) students in Bangladesh. An anonymous, self-administered questionnaire was sent to 640 PuU and 660 PrU students in Google Form between 25th September and 22nd November 2021, which resulted in the participation of 1034 (461 PuU vs. 573 PrU) respondents (response rate: 72.03% vs. 86.81%). The pooled vaccine acceptance rates among PuU and PrU students were almost similar (88.1%, 95% confidence interval (CI) 85.1–91.1 vs. 87.6%, 95% CI 84.6–90.6). Employing binary logistic regression to assess the association between various potential factors and vaccine acceptance, the study revealed that out of 10 predictors, ‘safety’ and ‘efficacy’ had highly significant positive associations with vaccine acceptance in both cohorts (P = 0.000, P = 0.005). ‘Political roles’ was found to have varied effects– a significant (P = 0.02) negative and a significant positive (P = 0.002) association with vaccine acceptance in PuU and PrU students, respectively. Additionally, ‘communication’ (P = 0.003) and ‘trust’ (P = 0.01) were found to have significant positive associations in PrU students while ‘rumours’ (P = 0.03) had negative association in PuU students. The odds of accepting the COVID-19 vaccine were 1.5 vs. 0.9 in PuU and PrU students. Although chi-square analysis did not show any significant association between gender and vaccine acceptance, discrepancies were found in the factors that potentially affect vaccine uptake decision between PuU and PrU students. COVID-19 vaccine uptake may be improved if vaccine-related information becomes available and is communicated to large numbers of people effectively. The implementation of multidisciplinary interventional educational programmes may also be considered as a preferred approach to improve student's engagement in pandemic awareness and vaccine readiness.

Resistance to beta-lactam antimicrobials caused by extended-spectrum beta-lactamase (ESBL)-producing organisms is a global health concern. The objectives of this study were to (1) summarise the prevalence of potential ESBL-producing Escherichia coli (ESBL-EC) and Salmonella spp. (ESBL-SA) isolates from agrifood and human sources in Canada from 2012 to 2017, and (2) describe the distribution of ESBL genotypes among these isolates. All data were obtained from the Canadian Integrated Program for Antimicrobial Resistance Surveillance (CIPARS). CIPARS analysed samples for the presence of ESBLs through phenotypic classification and identified beta-lactamase genes (blaTEM, blaSHV, blaCTX, blaOXA, blaCMY−2) using polymerase chain reaction (PCR) and whole genome sequencing (WGS). The prevalence of PCR-confirmed ESBL-EC in agrifood samples ranged from 0.5% to 3% across the surveillance years, and was detected most frequently in samples from broiler chicken farms. The overall prevalence of PCR-confirmed ESBL-SA varied between 1% and 4% between 2012 and 2017, and was most frequently detected in clinical isolates from domestic cattle. The TEM-CMY2 gene combination was the most frequently detected genotype for both ESBL-EC and ESBL-SA. The data suggest that the prevalence of ESBL-EC and ESBL-SA in Canada was low (i.e. <5%), but ongoing surveillance is needed to detect emerging or changing trends.

New SARS-CoV-2 variants causing COVID-19 are a major risk to public health worldwide due to the potential for phenotypic change and increases in pathogenicity, transmissibility and/or vaccine escape. Recognising signatures of new variants in terms of replacing growth and severity are key to informing the public health response. To assess this, we aimed to investigate key time periods in the course of infection, hospitalisation and death, by variant. We linked datasets on contact tracing (Contact Tracing Advisory Service), testing (the Second-Generation Surveillance System) and hospitalisation (the Admitted Patient Care dataset) for the entire length of contact tracing in the England – from March 2020 to March 2022. We modelled, for England, time delay distributions using a Bayesian doubly interval censored modelling approach for the SARS-CoV-2 variants Alpha, Delta, Delta Plus (AY.4.2), Omicron BA.1 and Omicron BA.2. This was conducted for the incubation period, the time from infection to hospitalisation and hospitalisation to death. We further modelled the growth of novel variant replacement using a generalised additive model with a negative binomial error structure and the relationship between incubation period length and the risk of a fatality using a Bernoulli generalised linear model with a logit link. The mean incubation periods for each variant were: Alpha 4.19 (95% credible interval (CrI) 4.13–4.26) days; Delta 3.87 (95% CrI 3.82–3.93) days; Delta Plus 3.92 (95% CrI 3.87–3.98) days; Omicron BA.1 3.67 (95% CrI 3.61–3.72) days and Omicron BA.2 3.48 (95% CrI 3.43–3.53) days. The mean time from infection to hospitalisation was for Alpha 11.31 (95% CrI 11.20–11.41) days, Delta 10.36 (95% CrI 10.26–10.45) days and Omicron BA.1 11.54 (95% CrI 11.38–11.70) days. The mean time from hospitalisation to death was, for Alpha 14.31 (95% CrI 14.00–14.62) days; Delta 12.81 (95% CrI 12.62–13.00) days and Omicron BA.2 16.02 (95% CrI 15.46–16.60) days. The 95th percentile of the incubation periods were: Alpha 11.19 (95% CrI 10.92–11.48) days; Delta 9.97 (95% CrI 9.73–10.21) days; Delta Plus 9.99 (95% CrI 9.78–10.24) days; Omicron BA.1 9.45 (95% CrI 9.23–9.67) days and Omicron BA.2 8.83 (95% CrI 8.62–9.05) days. Shorter incubation periods were associated with greater fatality risk when adjusted for age, sex, variant, vaccination status, vaccination manufacturer and time since last dose with an odds ratio of 0.83 (95% confidence interval 0.82–0.83) (P value < 0.05). Variants of SARS-CoV-2 that have replaced previously dominant variants have had shorter incubation periods. Conversely co-existing variants have had very similar and non-distinct incubation period distributions. Shorter incubation periods reflect generation time advantage, with a reduction in the time to the peak infectious period, and may be a significant factor in novel variant replacing growth. Shorter times for admission to hospital and death were associated with variant severity – the most severe variant, Delta, led to significantly earlier hospitalisation, and death. These measures are likely important for future risk assessment of new variants, and their potential impact on population health.

The rubella disease burden in Zambia may be under-estimated. Using models, we describe the transmission dynamics, determine the incidence estimates and assess the level of underestimation of the real burden of rubella infection in Zambia during the pre-vaccination period 2005–2016. This study used both the deterministic compartmental model and likelihood-based method using a Bayesian framework to describe the epidemiology of rubella. A total of 1313 cases of rubella were confirmed with the highest annual number of 255 new cases recorded in 2008. However, 2014 recorded the highest monthly median positivity rate of 9.0%. The observed median rubella cases were 5.5. There was a seasonal pattern in the occurrence of laboratory-confirmed rubella, with higher test positivity rates of rubella infection usually recorded in the months of September, October and November. The modelled monthly median incidence of rubella infection among the general population was 76 and 20 among pregnant women. The incidence of rubella among the non-pregnant women was 44. The average effective reproductive number (Rt) between 2005 and 2016 was estimated as 1.2 with the peak of infection occurring in 2016. The measles surveillance system underestimates the observed burden of rubella. A mass vaccination campaign conducted between January and July is recommended.

We study large sample properties of likelihood ratio tests of the unit-root hypothesis in an autoregressive model of arbitrary order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order 1, but resorted to a plug-in approach when dealing with higher-order models. In contrast, we consider the full model and derive the relevant large sample properties of likelihood ratio tests under a local-to-unity asymptotic framework. As in the simpler model, we show that the full likelihood ratio tests are nearly efficient, in the sense that their asymptotic local power functions are virtually indistinguishable from the Gaussian power envelopes. Extensions to sieve-type approximations and different classes of alternatives are also considered.

The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis–Hastings (MH) algorithms. Recently, acceptance probabilities other than MH are being employed in problems with intractable target distributions. There are few resources available on tuning the Gaussian proposal distributions for this situation. We obtain optimal scaling results for a general class of acceptance functions, which includes Barker’s and lazy MH. In particular, optimal values for Barker’s algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy.

Quantitative information on epidemiological quantities such as the incubation period and generation time of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants is scarce. We analysed a dataset collected during contact tracing activities in the province of Reggio Emilia, Italy, throughout 2021. We determined the distributions of the incubation period for the Alpha and Delta variants using information on negative polymerase chain reaction tests and the date of last exposure from 282 symptomatic cases. We estimated the distributions of the intrinsic generation time using a Bayesian inference approach applied to 9724 SARS-CoV-2 cases clustered in 3545 households where at least one secondary case was recorded. We estimated a mean incubation period of 4.9 days (95% credible intervals, CrI, 4.4–5.4) for Alpha and 4.5 days (95% CrI 4.0–5.0) for Delta. The intrinsic generation time was estimated to have a mean of 7.12 days (95% CrI 6.27–8.44) for Alpha and of 6.52 days (95% CrI 5.54–8.43) for Delta. The household serial interval was 2.43 days (95% CrI 2.29–2.58) for Alpha and 2.74 days (95% CrI 2.62–2.88) for Delta, and the estimated proportion of pre-symptomatic transmission was 48–51% for both variants. These results indicate limited differences in the incubation period and intrinsic generation time of SARS-CoV-2 variants Alpha and Delta compared to ancestral lineages.