We develop a decision-support framework for cyber risk mitigation policies from the perspective of an organization with limited resources for security controls, upgrades, and cyber insurance. To balance the conflicting optimization objectives of the organization and the insurer, we propose a bi-level model that endogenously derives optimal strategies for both parties, accounting for key uncertainties underlying a cyber attack. We find that cyber insurance coverage increases with premium size, though this depends on the effectiveness of system upgrades. Notably, the latter has an ambiguous impact on the equilibrium budget allocation strategy and insurance contract design, such that a more effective upgrade need not attract a commensurately larger budget allocation. We further show that information asymmetry regarding the insurer’s risk aversion can lead the defender to a suboptimal budget allocation, resulting in higher realized losses relative to the symmetric-information benchmark.

We study the asymptotic behavior of the number of crossings by a one-dimensional diffusion of a threshold where the process exhibits stickiness. We distinguish three types of crossings and show that to each type corresponds a distinct asymptotic regime for the respective number-of-crossings statistic. We introduce notions of bouncing as the symmetric counterparts to crossings and show that the corresponding number-of-bouncings statistics share the same asymptotic properties as their crossings counterparts. We first prove the results for sticky Brownian motion, then extend them to sticky–reflected Brownian motion (where only bouncing is possible) and to sticky diffusions. As an application, we propose consistent estimators for the stickiness parameter of sticky diffusions and sticky–reflected Brownian motion.

As large language models (LLMs) increasingly shape decision-making, public discourse, education, healthcare, and governance, a critical question emerges: Whose values are these systems truly reflecting? While today’s generative AI systems demonstrate extraordinary capabilities, they also inherit hidden biases, ethical blind spots, and implicit assumptions embedded within their training data. Existing alignment approaches often remain opaque, resource-intensive, or insufficiently adaptive to diverse societal expectations.

This paper introduces a novel value-driven LLM framework designed to systematically uncover, quantify, and realign the implicit values embedded within LLMs toward socially desirable outcomes. Built upon the AI for Social Good (AIfSG) framework, our proposed methodology operationalizes ethical alignment across six critical domains: reasoning and interpretability, bias removal, transparency and accountability, security and privacy, moral and ethical observations, and public understanding. Using advanced embedding techniques, cosine-based value-difference metrics, and topic-weighted iterative fine-tuning, the framework transforms ethical alignment from an abstract aspiration into a measurable and actionable computational process.

To demonstrate adaptability across moral and regulatory paradigms, the framework evaluates two distinct reference value systems: the Ten Commandments and the General Data Protection Regulation (GDPR). Experimental results using open-source LLMs, including Llama 3.2 and Gemma 2, reveal substantial reductions in value misalignment, ranging from approximately 25% to 70% across ethical domains, while preserving model flexibility and scalability. Visualizations in value-embedding space further confirm significant convergence between original model outputs and socially aligned reference values after iterative realignment.

Beyond technical innovation, this work positions value alignment as a foundational challenge for the future governance of generative AI. The proposed framework functions both as a diagnostic instrument for identifying ethical gaps and as an intervention mechanism for adaptive value realignment, offering policymakers, developers, and institutions a scalable pathway toward transparent, accountable, and socially responsible AI systems. By bridging computational methods with moral, legal, and societal principles, this research advances a new paradigm for embedding human-centered values directly into the next generation of intelligent systems.

Let $\mathrm{P}_K(n)$ be the probability that n points $z_1,\ldots,z_n$ picked uniformly and independently in K, a compact convex polygon in $\mathbb{R}^2$ with non-empty interior, are in convex position, that is, form the vertex set of a convex polygon. In this paper, the exact asymptotic behaviour of $\mathrm{P}_K(n)$ is determined as $n\to+\infty$. This improves on a famous result of Bárány [1999 Ann. Probab. 27, 2020–2034] (yet valid for a general convex set K) and a result initiated in the case where K is a regular convex polygon (Morin [2025 Adv. Appl. Probab. 57, 811–870]).

This is very important to prioritize nodes for immunization in controlling infectious disease outbreaks. In this paper, we propose a new immunization strategy for multiplex networks; we specifically model two separate layers: the physical layer where infection propagates and the virtual layer where information is transmitted. We assume that each layer has a different “context” and use that to identify the most suitable centrality measure for each. For the infection layer, we choose PageRank, as it has shown certain effectiveness in determining those nodes crucial for reducing transmission. For the awareness layer, we show how closeness centrality is a better measure of quality for the passing of information along short paths. We, therefore, propose Multiplex Combined PageRank, or MCPR, combining the centralities from both layers to immunize the most important nodes. The simulations employ the extended SIR-UA model, which exploits the interaction between infection and awareness dynamics, to scenarios on measles and smallpox. Validation on both synthetic networks and the real-world Copenhagen Networks Study dataset demonstrates consistent superiority of MCPR over classical methods. In terms of epidemic size in simulations with very limited immunization budgets, MCPR indeed resulted in better outcomes than the single-layer PageRank immunization strategy and the existing Multiplex PageRank method. Real-world validation shows epidemic size reductions of 2.2% for measles and 7% for smallpox at 10% immunization coverage, with parameter optimization yielding improvements up to 9.5%. The sensitivity analysis demonstrates that increasing transmission of awareness and the quality of information can help control the infection immensely.

Underwater three-dimensional (3D) scanning systems play a crucial role in marine archaeology, offshore engineering, and underwater robotics by capturing detailed representations of areas of interest. However, conventional underwater scanning methods are often time-consuming and inefficient, frequently collecting redundant data points that add little value to the overall representation. This study introduces an artificial intelligence (AI)-driven approach to underwater surface scanning that leverages machine learning techniques such as Bayesian optimisation and Gaussian Process regression to address these inefficiencies. A prototype 3D scanner, controlled by machine learning algorithms, was developed and tested in laboratory conditions that replicated the conditions of offshore deployment. Surfaces with different geometries, including flat, conical, and wavy shapes, were scanned to evaluate the performance of the proposed method against traditional approaches. The new scanning method autonomously selects the most informative measurement locations, reducing the number of scans required while exceeding the accuracy of conventional techniques. The results demonstrate that the proposed approach provides more precise surface representations for most geometries while significantly reducing scanning time. The approach not only reduces computational and storage requirements but also enables efficient data transmission in low-bandwidth scenarios, such as with underwater wireless communication systems. This research highlights the potential of machine learning-enhanced scanning systems to outperform traditional methods, offering a faster, more adaptable, and more accurate solution for underwater visualization in diverse scientific and engineering applications.

The paper investigates a non-zero-sum differential investment and reinsurance problem between two alpha-robust, risk-averse competitive insurers under a time-consistent mean-variance criterion. The claim arrival processes for both insurers follow the classical Cram’er–Lundberg model, and the reinsurance premium is calculated using the variance premium principle. Each insurer can invest its surplus in one risk-free asset, one risky asset, and a defaultable corporate bond. The paper also considers the effect of bounded memory, which is characterized by the wealth process with delay. Using the game-theoretic approach, we derive the non-zero-sum differential alpha-robust equilibrium strategy and the corresponding value function by solving the extended Hamilton–Jacobi–Bellman equation system. In the numerical simulation section, we observe a phenomenon where the optimal strategy for investing in defaultable bonds decreases as the competitor’s risk aversion coefficient increases, provided that one’s own risk aversion coefficient remains constant. However, when there is a change in one’s own risk aversion coefficient, even if the competitor’s risk aversion changes in the opposite direction, the optimal investment strategy in defaultable bonds still decreases as one’s own risk aversion coefficient increases.

We investigate branching processes in a nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely; therefore, we either condition on non-extinction or add inhomogeneous immigration. Extending our one-dimensional limit results from Kevei and Kubatovics (2024), we derive functional limit theorems. In the former case, the limit process is a time-changed simple birth-and-death process on $(-\infty, \infty)$ conditioned on survival at 0, while in the latter, it is a time-changed stationary continuous-time Markov branching process with immigration.

Climate change is expected to significantly affect the physical, financial, and economic environments over the long term, posing risks to the financial health of general insurers. While general insurers typically use Dynamic Financial Analysis (DFA) for a comprehensive view of financial impacts, traditional DFA as presented in the literature does not consider the impact of climate change. To address this gap, we extend the stationary DFA framework to integrate climate risk, enabling a holistic assessment of the long-term impact of climate change on the general insurance industry and offering a foundational architecture for the DFA of individual insurers. Our framework captures the long-term impact of climate change on the assets and liabilities of general insurers by considering both physical and economic dimensions across different climate scenarios within an interconnected structure. Furthermore, it addresses the uncertainty of climate change impacts using stochastic simulations within climate scenario analysis that are useful for actuarial applications. Our extensions are tailored to the general insurance sector and address its unique characteristics. To demonstrate the practical application of our model, we conduct an extensive empirical study using Australian data and assess the long-term financial impact of climate change on the general insurance market under various climate scenarios. The results are benchmarked against those of a stationary DFA framework and show that the interaction between economic growth and physical risk plays a key role in shaping general insurers’ risk–return profiles. They highlight the advantages of the climate-dependent DFA over the stationary DFA in generating financial projections under climate change impacts. Limitations of our framework are thoroughly discussed.

Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when an infinite state Markov chain is truncated and replaced with a finite-state approximation. Another situation of such approximations is when $P_{\infty}$ is a simplified limiting approximation to $P_n$ when n is large. In both settings, it is often verified that the approximation $P_n$ has the characteristic that its stationary distribution $\pi_n$ converges to the stationary distribution $\pi_{\infty}$ associated with the limit. We show that when the state space is countably infinite, this stationary distribution convergence implies that $P_n^m$ can be approximated uniformly in m by $P_{\infty}^m$ when n is large. We show that this ability to approximate the marginal distributions at all time scales m fails in continuous state space, but is valid when the convergence is in total variation or when we have weak convergence and the kernels are suitably Lipschitz. When the state space is discrete (as in the truncation setting), we further show that stationary distribution convergence also implies that all the expectations that are computable via first transition analysis (e.g. mean hitting times, expected infinite horizon discounted rewards) converge to those associated with the limit $P_{\infty}$. Simply put, we show that once we have established stationary distribution convergence, we can immediately infer convergence for a large range of other expectations.