In this paper, we provide a new property of value at risk (VaR), which is a standard risk measure that is widely used in quantitative financial risk management. We show that the subadditivity of VaR for given loss random variables holds for any confidence level if and only if those are comonotonic. This result also gives a new equivalent condition for the comonotonicity of random vectors.

In this paper, we study a two-period optimal insurance problem for a policyholder with mean-variance preferences who purchases proportional insurance at the beginning of each period. The insurance premium is calculated by a variance premium principle with a risk loading that depends on the policyholder’s claim history. We derive the time-consistent optimal insurance strategy in closed form and the optimal constant precommitment strategy in semiclosed form. For the optimal general precommitment strategy, we obtain the solution for the second period semi-explicitly and, then, the solution for the first period numerically via an efficient algorithm. Furthermore, we compare the three types of optimal strategies, highlighting their differences, and we examine the impact of the key model parameters on the optimal strategies and value functions.

As social media continues to grow, understanding the impact of storytelling on stakeholder engagement becomes increasingly important for policymakers and organizations who wish to influence policymaking. While prior research has explored narrative strategies in advertising and branding, researchers have paid scant attention to the specific influence of stories on social media stakeholder engagement. This study addresses this gap by employing Narrative Transportation Theory (NTT) and leveraging Natural Language Processing (NLP) to analyze the intricate textual data generated by social media platforms. The analysis of 85,075 Facebook publications from leading Canadian manufacturing companies, using Spearman’s rank correlation coefficient, underscores that individual storytelling components—character, sequence of events, and setting—along with the composite narrative structure significantly enhance stakeholder engagement. This research contributes to a deeper understanding of storytelling dynamics in social media, emphasizing the importance of crafting compelling stories to drive meaningful stakeholder engagement in the digital realm. The results of our research can prove useful for those who wish to influence policymakers or for policymakers who want to promote new policies.

A predictive column chart was developed to assess the risk of primary liver cancer (PLC) in hepatitis B patients. Data from 107 PLC patients and 107 controls were used as the training set, with 92 patients as the validation set. An additional 446 patients from other hospitals, including 15 with PLC, formed the external validation group. Multivariate logistic regression identified gender, BMI, alcohol consumption, diabetes, family history of liver cancer, cirrhosis, and HBV DNA load as independent risk factors. The model showed strong discrimination with AUCs of 0.882 and 0.859 in the training and validation sets, respectively, and good calibration (Hosmer–Lemeshow χ² = 2.648, P = 0.954; χ² = 4.117, P = 0.846). Decision curve analysis (DCA) confirmed clinical benefit within a risk threshold of 0.07–0.95. In the external validation group, the model maintained discrimination (AUC = 0.863) and calibration (Hosmer–Lemeshow χ² = 7.999, P = 0.434), with DCA showing net benefit across 0.14–0.95. These results indicate the column chart is a reliable tool for PLC risk prediction in hepatitis B patients.

We introduce a novel class of bivariate common-shock discrete phase-type (CDPH) distributions to describe dependencies in loss modeling, with an emphasis on those induced by common shocks. By constructing two jointly evolving terminating Markov chains that share a common evolution up to a random time corresponding to the common shock component, and then proceed independently, we capture the essential features of risk events influenced by shared and individual-specific factors. We derive explicit expressions for the joint distribution of the termination times and prove various class and distributional properties, facilitating tractable analysis of the risks. Extending this framework, we model random sums where aggregate claims are sums of continuous phase-type random variables with counts determined by these termination times and show that their joint distribution belongs to the multivariate phase-type or matrix-exponential class. We develop estimation procedures for the CDPH distributions using the expectation-maximization algorithm and demonstrate the applicability of our models through simulation studies and an application to bivariate insurance claim frequency data. In particular, the distribution of the latent common shock component present in correlated count data can be estimated as well.

Despite significant advances in Building Information Modeling (BIM) and increased adoption, numerous challenges remain. Discipline-specific BIM software tools with file storage have unresolved interoperability issues and do not capture or express interdisciplinary design intent. This hobbles machines’ ability to process design information. The lack of suitable data representation hinders the application of machine learning and other data-centric applications in building design. We propose Building Information Graphs (BIGs) as an alternative modeling method. In BIGs, discipline-specific design models are compiled as subgraphs in which nodes and edges model objects and their relationships. Additional nodes and edges in a meta-graph link the building objects across subgraphs. Capturing both intradisciplinary and interdisciplinary relationships, BIGs provide a dimension of contextual data for capturing design intent and constraints. BIGs are designed for computation and applications. The explicit relationships enable advanced graph functionalities, such as across-domain change propagation and object-level version control. BIGs preserve multimodal design data (geometry, attributes, and topology) in a graph structure that can be embedded into high-dimensional vectors, in which learning algorithms can detect statistical patterns and support a wide range of downstream tasks, such as link prediction and graph generation. In this position article, we highlight three key challenges: encapsulating and formalizing object relationships, particularly design intent and constraints; designing graph learning techniques; and developing innovative domain applications that leverage graph structures and learning. BIGs represent a paradigm shift in design technologies that bridge artificial intelligence and building design to enable intelligent and generative design tools for architects, engineers, and contractors.

Over 193 countries have signed at least one of more than 500 multilateral treaties addressing critical global issues, such as human rights, environmental protection, and trade. Ratifying a treaty obligates a country, as a “State Party,” to report to the United Nations on its progress toward implementing the treaty’s provisions. These reports and their associated review processes generate a wealth of textual data. Effectively monitoring, reviewing, and assessing national, regional, and global progress toward these treaty commitments is crucial for ensuring compliance and realizing the benefits of international cooperation. The UN Convention on the Rights of Persons with Disabilities (CRPD), which has been ratified by 191 countries, exemplifies this challenge. With over 1.3 billion people worldwide living with disabilities, the CRPD aims to promote a shift from a charity-based “medical model” that views disability as an individual deficiency, to a rights-based “social justice model” that emphasizes societal barriers and inclusivity. Each State Party submits periodic reports to the Committee on the Rights of Persons with Disabilities detailing their implementation efforts. This study analyzed all available CRPD State Reports (N = 170) using text mining, Natural Language Processing, and GenerativeAI tools to assess global progress, identify regional variations, and explore the factors influencing successful implementation. The findings reveal evidence of widespread CRPD implementation, growing support for social justice and economic inclusion, and the importance of civil society engagement. Hybrid data analysis approach of this study offers a promising framework for harnessing the power of textual data to advance the realization of treaty commitments worldwide.