Relative entropy, as a divergence metric between two distributions, can be used for offline change-point detection and extends classical methods that mainly rely on moment-based discrepancies. To build a statistical test suitable for this context, we study the distribution of empirical relative entropy and derive several types of approximations: concentration inequalities for finite samples, asymptotic distributions, and Berry--Esseen bounds in a pre-asymptotic regime. For the latter, we introduce a new approach to obtain Berry--Esseen inequalities for nonlinear functions of sum statistics under some convexity assumptions. Our theoretical contributions cover both one- and two-sample empirical relative entropies. We then detail a change-point detection procedure built on relative entropy and compare it, through extensive simulations, with classical methods based on moments or on information criteria. In particular, we show that our method has a high power for many types of change-points. Finally, we illustrate the practical relevance of our method on a real dataset involving time series of volatility of stock indices, namely several realized volatility series as well as the VIX. In this application, we define the change-point as a modification of the multivariate distribution of successive increments of volatility. Therefore, every detection of a change-point highlights a modification of the serial dependence of volatility and thus a modification of the way people should predict this risk measure.

Organizations executing multiple concurrent projects frequently face operational risks due to material shortages, idle inventory, emergency procurement, and fragmented decision-making. While traditional ERP systems optimize procurement within individual projects, they offer limited support for structured cross-project redistribution under uncertainty. This study proposes CIRIS (Cross-Inventory Reallocation & Intelligence System), a risk-aware framework designed to enhance supply chain resilience and reduce capital inefficiencies through structured decision modeling.

CIRIS is implemented as a hybrid desktop–cloud architecture with offline-first capability and centralized synchronization. The framework is built on a configurable multi-factor reallocation model, where candidate resource transfers are evaluated using weighted parameters including urgency, item criticality, historical usage trends, geographical proximity, transfer cost, and expected risk reduction. These parameters are normalized and aggregated into a composite priority score to rank feasible redistribution actions. The system further integrates three analytical components: a Shortage Probability Predictor, an Idle Capital Risk Index, and a Cross-Project Resilience Indicator. An event-driven workflow with QR-enabled chain-of-custody tracking ensures traceability and auditability.

Prototype validation is conducted using synthetic multi-project datasets under simulated disruption scenarios, including demand spikes and supply delays. The results indicate that CIRIS effectively identifies surplus–shortage relationships, prioritizes reallocation decisions, and improves internal resource utilization while reducing dependency on emergency procurement.

CIRIS extends conventional inventory systems into a structured risk intelligence framework for multi-project environments, providing a scalable foundation for enterprise deployment and future empirical validation.

The energy sector depends on high-value, safety-critical assets where failures can result in severe human, environmental, and financial consequences. Although insurance provides financial risk transfer, current underwriting practices largely rely on historical loss data and regional benchmarks, often overlooking asset-specific integrity conditions and management effectiveness. Risk-Based Inspection (RBI) offers a structured engineering approach to quantify probability and consequence of failure at the asset level, yet its outputs are rarely integrated into insurance premium determination.

This study introduces a Risk-Based Premium Model (RBPM) framework that embeds RBI outputs and integrity management data directly into insurance pricing. The framework prioritizes inspection confidence and documented integrity management practices as primary premium drivers, with remaining asset life applied as a secondary modifier. Aboveground Storage Tank datasets from prior integrity studies, including inspection histories, condition assessments, and management plans, were used to test the model and compare premium outcomes across differing risk profiles.

Application of RBPM demonstrated clear differentiation between well-managed and poorly managed assets. Tanks with low remaining life but high inspection confidence and active integrity management plans were rated comparably to lower-risk assets, reflecting reduced uncertainty. Conversely, assets with unknown condition, limited inspection coverage, or absent management strategies attracted significant premium loadings. The model replaced generic actuarial assumptions with transparent, evidence-based engineering risk indicators.

RBPM establishes a direct link between integrity risk reduction and financial reward, promoting proactive asset management while reducing insurer uncertainty. By aligning engineering reliability with insurance economics, the framework enables fairer, condition-based premiums and incentivizes continuous integrity improvement. Future work includes integration with digital twins, real-time analytics, and standardized RBI–insurance protocols to further enhance risk-responsive underwriting.

Ghana’s Basic National Social Security Scheme (Tier 1), managed by the Social Security and National Insurance Trust (SSNIT), faces sustainability challenges due to shifting pension demographics and macro-financial volatility. Using optimal control theory, our paper formulates a continuous-time stochastic control problem for a social planner (SSNIT) to determine optimal policies of investment and benefit indexation that maximize discounted expected utility of aggregate retiree benefits over a finite horizon, subject to ruin probability constraint with a solvency floor. The dynamics of the pension fund’s asset under management combine risky and risk-free investment returns with stochastic net cashflows driven by a CEV salary process and deterministic contributor and retiree population flows. Using the principle of dynamic programming (Bellman’s optimality condition), we derive the associated Hamilton–Jacobi–Bellman PDE and obtain feedback characterizations of the optimal portfolio and indexation policies under Karush–Kuhn–Tucker (KKT) control bounds. We couple the optimal feedback policy with a backward Kolmogorov survival probability to enforce the chance constraint. The numerical results, calibrated using the trustee’s (SSNIT) data and Ghana’s financial market inputs over a 30-year planning horizon, yielded an optimal asset allocation mix of 19.5% equity exposure and 9.9% benefit indexation at 96.7% survival probability for sustainability. The results further show that a 0.5% increase in the contribution rate as a policy modification doubles benefit adequacy at 10% equity exposure and 15% benefit indexation with 99% sustainability. Similarly, a 1% increase in contribution rate yielded no additional adequacy gains beyond the 0.5% increment but improved survival probability to 99.9%. These findings suggest that modest, targeted contribution-rate adjustments combined with disciplined asset allocation provide a quantitatively superior pathway to restoring long-term sustainability without sacrificing intergenerational benefit adequacy.

Background: Accurate forecasting of realized volatility (RV) remains a cornerstone of risk management and option pricing. Hybrid volatility models, such as the HAR-RV-CARMA framework, have proven effective at fusing discrete-time persistence with continuous-time dynamics, utilizing the standard Kalman Filter for weight allocation. The model operates on a reactive feedback loop that relies on past residuals, often leading to a "tracking lag" during rapid market transitions, in which the model fails to shift weights quickly enough among its constituent components.

Methods: This study introduces a novel architectural enhancement to the HAR-RV-CARMA model by adding an Entropy-Conditioned State-Space Layer. We utilize Sample Entropy as an external complexity indicator to track the information regularity of the volatility series in real time. By linking entropy fluctuations to the noise covariance system in the Kalman Filter, we create a proactive regime-switching mechanism. This enables the model to identify breakdowns in structural persistence and speed up weight re-adjustments before prediction errors accumulate in full.

Results: Using daily realized volatility for major U.S. equity ETFs (SPY, QQQ, and IWM), the models are estimated over a training period from 2015 to 2022 and a test period covering 2023 to 2024. The proposed entropy-conditioned hybrid model is assessed against the base HAR-RV-CARMA model. Forecast performance is evaluated using MAE, MSE, QLIKE, and directional accuracy. The results show that the entropy-enhanced model consistently outperforms the base hybrid model across all evaluation metrics.

Conclusion: Overall, the proposed framework offers a flexible and econometrically sound approach to volatility forecasting that balances model simplicity with regime-sensitive learning. The Entropy-Conditioned HAR-RV-CARMA model effectively reduces the lag present in standard dynamic weighting, providing a more robust forecasting tool for highly volatile markets.

Accurately forecasting bankruptcies within the financial sector is an essential objective for prudential regulators tasked with maintaining financial stability. While Machine Learning techniques, in particular the more advanced ensemble methods, and neural networks have been proven to perform well in forecasting loan defaults, these methods have yet to be integrated into workflows for assessing the risk and predicting the failure of financial institutions.

To identify the most effective approach to predicting the default of banks and NBFIs, this study investigates the performance of eight leading predictive modeling techniques of varying complexity—from traditional statistical models to advanced Machine Learning methods against Large Language Models (LLMs), a rapidly growing area of Artificial Intelligence.

The paper develops a new workflow that uses LLMs to analyze the risk exposure of financial institutions and determine their probability of default. A new PD metric, that LLMs are capable of generating accurately, is created as the joint outcome of risk and profitability, whose impacts are separately estimated by the model. To further improve the analysis, the paper proposes a new financial performance indicator and adaptations for traditional ratios to enable their usage in both going concern and failure contexts.

The results of the study reveal that while traditional methods like regression models and Random Forests can provide very good predictive capabilities, the best performance is achieved with the Large Language Model, which significantly surpasses all other methods in the majority of evaluation metrics. The LLM's ability to capture complex patterns and contextual nuances within financial data results in superior predictive accuracy and robustness. This highlights the potential of incorporating advanced language-based modeling approaches into financial risk management systems, paving the way for more intelligent and adaptive frameworks that enhance decision-making and regulatory policy in the financial industry.

The increasing frequency of anomalous climatic events exposes energy utilities to significant volumetric risk, particularly through revenue shortfalls during mild winters. To hedge this exposure, firms rely on Over-the-Counter weather derivatives, such as Heating Degree Day (HDD) options, structured as weighted spatial baskets that reflect distributed customer loads. Pricing and risk-managing these multi-site contracts remains challenging due to spatial dependence structures in temperature dynamics. Existing pricing frameworks fall into two categories. First, modelling each geographical location independently ignores the spatial correlation of weather phenomena. This creates a false sense of portfolio diversification, cancelling out local shocks and underestimating portfolio risk. Second, to manage spatial dependence, the literature relies on linear techniques driven by empirical covariance matrices. While mathematically convenient, these linear transformations struggle to capture asymmetric tail dependencies and climatic extremes, implying theoretical hedging baskets that are untradable in illiquid weather markets. These frameworks are bound to discrete meteorological stations or fixed grids, inducing basis risk when evaluating portfolios tied to off-grid locations, highlighting an unmet need for continuous spatial representations. To address these limitations, we propose a neural network framework designed to price temperature derivatives under interdependent risks. Our network architecture performs non-linear dimensionality reduction, compressing the high-dimensional field into latent risk factors. By utilising a continuous spatial approach, we map these latent factors to any geographic coordinate, solving the spatial discretisation problem. This design preserves explainability essential for risk management, while capturing asymmetric spatial interactions and tail dependencies that linear covariance models miss. Empirical analysis on NASA MERRA-2 temperature data demonstrates that our interpretable approach captures spatial risk dependence more accurately than linear models. This leads to improved pricing stability, reliable portfolio Value-at-Risk estimates, and hedging performance for multi-site HDD options, highlighting the critical role of explainable non-linear spatial modelling in climate-related financial risk.

Introduction
Cyber ​​insurance markets are fertile ground for outcome-based contracts (OBCs), in which premiums depend on observable security performance. While these contracts aim to align incentives between policyholders and insurance companies, they also introduce additional solvency risk due to the stochastic interaction between security investments, loss frequency, and premium variability. Therefore, we propose a stochastic framework to model the trade-off between policyholders' security investments and insurer liability and to assess the solvency implications of performance-related pricing in cyber insurance.

Methods
We extend a stochastic Gordon–Loeb framework with aggregate losses dependent on the stochastic breach probability determined by security investments. The policyholder's investment dynamics are modeled as an exogenous mean-reverting diffusion, which captures operational uncertainty. The insurance company offers a premium adjustment based on expected outcomes, linked to vulnerability over the contractual horizon. The insurance company's profit and loss distribution is derived by combining the frequency of stochastic attacks, their severity, vulnerability dynamics, and performance-related premium variability. This also allows for the effects on capital requirements.

Expected Results
The model reveals a nonlinear relationship between incentive intensity and capital requirements. Performance-based pricing reduces expected losses but increases profit volatility due to premium variability. The net solvency effect depends on the covariance between aggregate losses and vulnerability-based premium adjustments. An optimal incentive intensity emerges that minimizes required capital while preserving risk mitigation benefits.

Conclusions
Outcome-based cyber insurance contracts create a measurable trade-off between security investment incentives and the insurer's solvency risk. The proposed framework enables dynamic performance-based pricing, consistent with risk-sensitive capital valuation, providing a quantitative basis for prudentially sound cyber OBC design.

Maritime piracy remains a persistent and geographically shifting threat to international shipping, generating direct losses (ransom payments, cargo theft, vessel damage) as well as substantial indirect costs related to delays, rerouting, insurance premiums, and private security measures. Despite a decline in high-profile incidents in some regions, the economic exposure of global supply chains to piracy risk remains significant, particularly along strategic chokepoints and in emerging high-risk zones. This study examines how piracy risk is identified, quantified, and incorporated into maritime risk portfolios by shipowners, insurers, and logistics operators. The paper develops an integrated economic framework for pricing maritime security under uncertainty. First, piracy risk is modeled using frequency–severity approaches commonly applied in actuarial science, incorporating spatial concentration, seasonal variation, and clustering effects. Second, cost components associated with preventive and reactive measures—armed guards, vessel hardening, convoy participation, rerouting, and kidnap and ransom (K&R) insurance—are analyzed as portfolio hedging instruments. Third, the study evaluates how piracy risk premiums are transferred along the value chain, affecting freight rates, charter agreements, and trade competitiveness. Using scenario analysis and sensitivity testing, the research compares optimal security investment strategies under varying attack probabilities and loss distributions. Results indicate that maritime security expenditures function as a hybrid financial–operational hedge, reducing tail risk while influencing overall portfolio volatility. Furthermore, diversification across routes and contract structures can mitigate concentrated exposure to piracy-prone areas. The findings contribute to financial risk management by positioning piracy not merely as a security issue but as a measurable economic variable that reshapes cost allocation and asset valuation in maritime transport. The study provides decision-support insights for insurers, shipowners, and policymakers seeking to balance security investments with capital efficiency in an evolving global risk environment.

Short-term mortality fluctuations are traditionally estimated using Serfling models [2], which capture trend and seasonality through Fourier harmonic components. Recent studies have highlighted the importance of climate in explaining mortality dynamics. Robben et al. (2024) [1] show that climate variables significantly improve weekly mortality prediction using machine learning techniques. This evidence suggests that climate contains relevant information for seasonal mortality dynamics. However, many approaches impose rigid seasonal structures or rely on black-box models, limiting interpretability. Moreover, spatial mortality models typically require the explicit specification of geographic dependence through spatial weight matrices. Motivated by these considerations, we introduce an interpretable deep-learning extension of the Serfling model in which climate effects are structurally incorporated into the seasonal dynamics. Our framework allows spatial heterogeneity to emerge directly from the learning architecture without requiring external spatial regularization. Specifically, we introduce feedforward neural networks that dynamically model the amplitudes of seasonal oscillations as a function of climate variables. This extension preserves the interpretability of the baseline framework while enabling nonlinear climate modulation. We use weekly mortality data for NUTS3 regions in Europe; models are estimated over 2014–2022 and evaluated out-of-sample in 2023.
Across multiple evaluation metrics, these extensions reveal consistent improvements in predictive performance over the baseline, with gains observed in more than half of the analyzed regions. These findings confirm the models’ ability to capture spatial heterogeneity and demonstrate the robustness of the proposed specification. The framework therefore provides an interpretable advancement for climate-sensitive risk analysis in actuarial applications.

References

[1] Robben, J., Antonio, K., & Kleinow, T. (2025). The short-term association between environmental variables and mortality: evidence from Europe. Journal of the Royal Statistical Society Series A: Statistics in Society, qnaf052.

[2] Serfling, R. E. (1963). Methods for current statistical analysis of excess pneumonia-influenza deaths. Public health reports, 78(6), 494.