We study several basic problems about colouring the $p$-random subgraph $G_p$ of an arbitrary graph $G$, focusing primarily on the chromatic number and colouring number of $G_p$. In particular, we show that there exist infinitely many $k$-regular graphs $G$ for which the colouring number (i.e., degeneracy) of $G_{1/2}$ is at most $k/3 + o(k)$ with high probability, thus disproving the natural prediction that such random graphs must have colouring number at least $k/2 - o(k)$.

Consider nested subdivisions of a bounded real set into intervals defining the digits $X_1,X_2,\ldots$ of a random variable X with a probability density function f. If f is almost everywhere lower semi-continuous, there is a non-negative integer-valued random variable N such that the distribution of $R=(X_{N+1},X_{N+2},\ldots)$ conditioned on $S=(X_1,\ldots,X_N)$ does not depend on f. If also the lengths of the intervals exhibit a Markovian structure, $R\mid S$ becomes a Markov chain of a certain order $s\ge0$. If $s=0$ then $X_{N+1},X_{N+2},\ldots$ are independent and identically distributed with a known distribution. When $s>0$ and the Markov chain is uniformly geometric ergodic, there is a random time M such that the chain after time $\max\{N,s\}+M-s$ is stationary and M follows a simple known distribution.

We introduce a financial market model featuring a risky asset whose price follows a sticky geometric Brownian motion and a riskless asset that grows with a constant interest rate $r\in \mathbb R$. We prove that this model satisfies no arbitrage and no free lunch with vanishing risk only when $r=0$. Under this condition, we derive the corresponding arbitrage-free pricing equation, assess the replicability, and give a representation of the replication strategy. We then show that all locally bounded replicable payoffs for the standard Black–Scholes model are also replicable for the sticky model. Last, we evaluate via numerical experiments the impact of hedging in discrete time and of misrepresenting price stickiness.

Tunnel boring machines (TBMs) are essential equipment for tunnel excavation. The main component of TBMs for breaking rock is the disc cutter. The effectiveness and productivity of TBM operations are directly impacted by the disc cutter design and performance. This study investigates the effects of confining stress on the breaking force of disc cutters with various diameters. Both saturated and dry rock, such as low-strength concrete, medium-strength marble, and high-strength granite, are used in the tests. It is found that disc cutters with larger diameter can reduce the influence of the confining stress. Moreover, this research indicates that the influence of confining stress is more notable in rocks with higher strengths, especially in dry condition as opposed to saturated condition. The failure load is related to the confining stress, cutter diameter, and compressive strength of the rock in a multivariate linear regression model, suggesting that the confining stress is more significant than the other variables. These results highlight the importance of considering in-situ stress conditions when excavating tunnels by TBMs.

We focus on obtaining Block–Savits type characterizations for different ageing classes as well as some important renewal classes by using the Laplace transform. We also introduce a novel approach, based on the equilibrium distribution, to handle situations where the techniques of Block and Savits (1980) either fail or involve tedious calculations. Our approach in conjunction with the theory of total positivity yields Vinogradov’s (1973) result for the increasing failure rate class when the distribution function is continuous. We also present simple but elegant proofs for Block and Savits’ results for the decreasing mean residual life, new better than used in expectation, and harmonic new better than used in expectation classes as applications of our approach. We address several other related issues that are germane to our problem. Finally, we conclude with a short discussion on the issue of convolutions.

We all know the importance of taking advice from the right people. In the financial services arena, good quality financial advice helps millions of people manage their money, realise their goals and achieve long-term financial security. Given the low level of financial literacy in the general population, financial advice can be seen as a necessity for millions of people. However, our brief research to date indicates that a huge advice gap has emerged in the UK following the introduction of the Retail Distribution Review in 2012. And it doesn’t look like this will get better soon. Regarding this advice gap, the FCA stated in 2023 that “the provision of financial advice is often out of reach for all but the already wealthy.” Furthermore, efforts to mitigate the advice gap are either non-existent or piecemeal at best.

The consequences of the advice gap include poor investment decisions leading to sub-optimal savings: research shows that consumers in the UK who took professional financial advice between 2001 and 2006 enjoyed an average increase in their assets of nearly £48,000 (∼20%) after ten years, compared to those who took no advice. In this paper, we consider various mechanisms to improve access to financial advice and guidance and reduce the size of the advice gap while recognising that these should be implemented under the umbrella of Consumer Duty, which should ensure that customers receive good outcomes.

Finally, in terms of financial inclusion, there is a gender and social imbalance with women and those from lower socio-economic groups less likely to access formal advice or guidance. This is where the advice gap is biggest, and some of these groups of people could benefit most from access to financial advice or guidance, particularly those groups with lower levels of financial literacy who have reduced means to start off with. Implementing measures to reduce the advice gap under the umbrella of a strong consumer duty should provide customers with the means to pay for the level of advice that they need while being confident that they are receiving the right products for their needs at the right price leading to good customer outcomes.

On both global and local levels, one can observe a trend toward the adoption of algorithmic regulation in the public sector, with the Chinese social credit system (SCS) serving as a prominent and controversial example of this phenomenon. Within the SCS framework, cities play a pivotal role in its development and implementation, both as evaluators of individuals and enterprises and as subjects of evaluation themselves. This study engages in a comparative analysis of SCS scoring mechanisms for individuals and enterprises across diverse Chinese cities while also scrutinizing the scoring system applied to cities themselves. We investigate the extent of algorithmic regulation exercised through the SCS, elucidating its operational dynamics at the city level in China and assessing its interventionism, especially concerning the involvement of algorithms. Furthermore, we discuss ethical concerns surrounding the SCS’s implementation, particularly regarding transparency and fairness. By addressing these issues, this article contributes to two research domains: algorithmic regulation and discourse surrounding the SCS, offering valuable insights into the ongoing utilization of algorithmic regulation to tackle governance and societal challenges.

Africa had a busy election calendar in 2024, with at least 19 countries holding presidential or general elections. In a continent with a large youth population, a common theme across these countries is a desire for citizens to have their voices heard, and a busy election year offers an opportunity for the continent to redeem its democratic credentials and demonstrate its leaning towards strengthening free and fair elections and a more responsive and democratic governance. Given the central role that governance plays in security in Africa, the stakes from many of these elections are high, not only to achieve a democratically elected government but also to achieve stability and development. Since governance norms, insecurity, and economic buoyancy are rarely contained by borders, the conduct and outcomes from each of these elections will also have implications for neighbouring countries and the continent overall. This article considers how the results of recent elections across Africa have been challenged in courts based on mistrust in the use of technology platforms, how the deployment of emerging technology, including AI, is casting a shadow on the integrity of elections in Africa, and the policy options to address these emerging trends with a particular focus on governance of AI technologies through a human rights-based approach and equitable public procurement practices.

Gastrointestinal infections significantly impact African low- and middle-income countries, although, accurate data on acute gastrointestinal illness (AGI) for all ages are lacking. This study aimed to describe the epidemiology of AGI in Ethiopia, Mozambique, Nigeria, and Tanzania. A population survey was conducted in one urban and one rural site per country, from 01 October 2020 to 30 September 2021, using web-based and face-to-face tools (n = 4417). The survey tool was adapted from high-income countries, ensuring comparability through an internationally recommended AGI case definition. Ethiopia had the highest AGI incidence (0.87 episodes per person-year), followed by Mozambique (0.58), Tanzania (0.41), and Nigeria (0.34). Age-standardized incidence was highest in Mozambique (1.46) and Ethiopia (1.25), compared to Tanzania (0.58) and Nigeria (0.33). The 4-week prevalence was 6.4% in Ethiopia and 4.3% in Mozambique, compared to 3.1% in Tanzania and 2.6% in Nigeria. AGI lasted an average of 5.3 days in Ethiopia and 3.0 to 3.4 days elsewhere. Children under five had 4.4 times higher AGI odds (95% CI: 2.8, 6.7) than those aged 15-59. The study provides empirical data on the incidence and demographic determinants of AGI in these four countries.

Hand, foot, and mouth disease (HFMD) shows spatiotemporal heterogeneity in China. A spatiotemporal filtering model was constructed and applied to HFMD data to explore the underlying spatiotemporal structure of the disease and determine the impact of different spatiotemporal weight matrices on the results. HFMD cases and covariate data in East China were collected between 2009 and 2015. The different spatiotemporal weight matrices formed by Rook, K-nearest neighbour (KNN; K = 1), distance, and second-order spatial weight matrices (SO-SWM) with first-order temporal weight matrices in contemporaneous and lagged forms were decomposed, and spatiotemporal filtering model was constructed by selecting eigenvectors according to MC and the AIC. We used MI, standard deviation of the regression coefficients, and five indices (AIC, BIC, DIC, R2, and MSE) to compare the spatiotemporal filtering model with a Bayesian spatiotemporal model. The eigenvectors effectively removed spatial correlation in the model residuals (Moran’s I < 0.2, p > 0.05). The Bayesian spatiotemporal model’s Rook weight matrix outperformed others. The spatiotemporal filtering model with SO-SWM was superior, as shown by lower AIC (92,029.60), BIC (92,681.20), and MSE (418,022.7) values, and higher R2 (0.56) value. All spatiotemporal contemporaneous structures outperformed the lagged structures. Additionally, eigenvector maps from the Rook and SO-SWM closely resembled incidence patterns of HFMD.

Predicting healthcare costs for chronic diseases is challenging for actuaries, as these costs depend not only on traditional risk factors but also on patients’ self-perception and treatment behaviors. To address this complexity and the unobserved heterogeneity in cost data, we propose a dual-structured learning statistical framework that integrates covariate clustering into finite mixture of generalized linear models, effectively handling high-dimensional, sparse, and highly correlated covariates while capturing their effects on specific subgroups. Specifically, this framework is realized by imposing a penalty on the prior similarities among covariates, and we further propose an expectation-maximization-alternating direction method of multipliers (EM-ADMM) algorithm to address the complex optimization problem by combining EM with the ADMM. This paper validates the stability and effectiveness of the framework through simulation and empirical studies. The results show that our framework can leverage shared information among high-dimensional covariates to enhance fitting and prediction accuracy, while covariate clustering can also uncover the covariates’ network relationships, providing valuable insights into diabetic patients’ self-perception data.

This article extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003, Econometrica 71(4), 1027-–1048) to instrumental variable regression models with unknown homoskedastic error variance and many weak instruments. We argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid in this setting. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that our modified test achieves asymptotic validity under many weak instruments asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003, Econometrica 71(4), 1027-–1048). A simulation study illustrates the desirable finite sample properties of our test.

We introduce the exponentially preferential recursive tree and study some properties related to the degree profile of nodes in the tree. The definition of the tree involves a radix $a\gt 0$. In a tree of size $n$ (nodes), the nodes are labeled with the numbers $1,2, \ldots ,n$. The node labeled $i$ attracts the future entrant $n+1$ with probability proportional to $a^i$.

We dedicate an early section for algorithms to generate and visualize the trees in different regimes. We study the asymptotic distribution of the outdegree of node $i$, as $n\to \infty$, and find three regimes according to whether $0 \lt a \lt 1$ (subcritical regime), $a=1$ (critical regime), or $a\gt 1$ (supercritical regime). Within any regime, there are also phases depending on a delicate interplay between $i$ and $n$, ramifying the asymptotic distribution within the regime into “early,” “intermediate” and “late” phases. In certain phases of certain regimes, we find asymptotic Gaussian laws. In certain phases of some other regimes, small oscillations in the asymototic laws are detected by the Poisson approximation techniques.

This paper introduces a method for pricing insurance policies using market data. The approach is designed for scenarios in which the insurance company seeks to enter a new market, in our case: pet insurance, lacking historical data. The methodology involves an iterative two-step process. First, a suitable parameter is proposed to characterize the underlying risk. Second, the resulting pure premium is linked to the observed commercial premium using an isotonic regression model. To validate the method, comprehensive testing is conducted on synthetic data, followed by its application to a dataset of actual pet insurance rates. To facilitate practical implementation, we have developed an R package called IsoPriceR. By addressing the challenge of pricing insurance policies in the absence of historical data, this method helps enhance pricing strategies in emerging markets.

Motivated by the investigation of probability distributions with finite variance but heavy tails, we study infinitely divisible laws whose Lévy measure is characterized by a radial component of geometric (tempered) stable type. We closely investigate the univariate case: characteristic exponents and cumulants are calculated, as well as spectral densities; absolute continuity relations are shown, and short- and long-time scaling limits of the associated Lévy processes analyzed. Finally, we derive some properties of the involved probability density functions.

Many pension plans and private retirement products contain annuity factors, converting the funds at some future time into lifelong income. In general model settings like, for example, the Li-Lee mortality model, analytical values for the annuity factors are not available and one has to rely on numerical techniques. Their computation typically requires nested simulations as they depend on the interest rate level and the mortality tables at the time of retirement. We exploit the flexibility and efficiency of feed-forward neural networks (NNs) to value the annuity factors at the time of retirement. In a numerical study, we compare our deep learning approach to (least-squares) Monte-Carlo, which can be represented as a special case of the NN.