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28 pages, 16306 KB  
Article
A Risk-Aware Supply Function Nash Equilibrium Framework for Strategic Bidding in Day-Ahead Electricity Markets
by Muhammad Muzammal Islam, Tianyou Yu, Massimo La Scala, Sergio Bruno, Ziqiang Wang, Cosimo Iurlaro and Andrea Altamura
Algorithms 2026, 19(8), 658; https://doi.org/10.3390/a19080658 - 9 Aug 2026
Viewed by 144
Abstract
Strategic bidding in day-ahead electricity markets requires generation companies to maximize expected profits while managing financial risks arising from market uncertainty and competitors’ strategic behavior. This paper proposes a game-theoretic risk-aware strategic bidding framework based on a Supply Function Nash Equilibrium (SFNE) for [...] Read more.
Strategic bidding in day-ahead electricity markets requires generation companies to maximize expected profits while managing financial risks arising from market uncertainty and competitors’ strategic behavior. This paper proposes a game-theoretic risk-aware strategic bidding framework based on a Supply Function Nash Equilibrium (SFNE) for dominant market operators in a uniform-pricing day-ahead market. Each operator strategically determines cluster-level bidding markups for its heterogeneous generation portfolio while anticipating competitors’ strategies. Demand uncertainty is represented by a finite scenario set, and Conditional Value-at-Risk (CVaR) of profit shortfall is incorporated into each operator’s expected-profit objective. The resulting non-cooperative equilibrium is solved using a relaxed Nikaido–Isoda (NI) best-response algorithm with convergence criteria based on the relative NI gap, strategy variation, and utility variation. The framework is validated using publicly available Italian day-ahead market offer data, where technology-oriented clustering reduces the strategic decision dimension while preserving portfolio heterogeneity. The proposed algorithm satisfies all convergence criteria within approximately 54 iterations. Numerical results show that the proposed risk-aware SFNE reduces aggregate downside-profit risk by approximately 7% compared with the risk-neutral SFNE while maintaining comparable expected profitability and slightly lowering market-clearing prices and procurement costs. A realistic 24 h market simulation further confirms the robustness and applicability of the proposed framework under time-varying market conditions. Overall, the proposed framework provides an economically interpretable and computationally tractable benchmark for risk-aware strategic bidding in day-ahead electricity markets. Full article
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32 pages, 1836 KB  
Article
Multivariate Scenario-Based Optimization Framework for Wind Power Bidding Curves with Heavy-Tailed Forecast Uncertainty
by Junghyeop Im, Minsoo Kim, Minkyu Jung, Hyeonjun Im and Duehee Lee
Mathematics 2026, 14(15), 2849; https://doi.org/10.3390/math14152849 - 6 Aug 2026
Viewed by 190
Abstract
Wind power producers face severe financial risks from intermittent generation and volatile prices. In this paper, we develop a multivariate scenario-based optimization framework that integrates heavy-tailed Laplace forecast-error path generation, principal component (PC) score matching, and Frequency-Concentrated Projection (FCP) to determine day-ahead bidding [...] Read more.
Wind power producers face severe financial risks from intermittent generation and volatile prices. In this paper, we develop a multivariate scenario-based optimization framework that integrates heavy-tailed Laplace forecast-error path generation, principal component (PC) score matching, and Frequency-Concentrated Projection (FCP) to determine day-ahead bidding curves that maximize expected settlements. To model uncertainty, 24-h scenarios are generated by sequentially accumulating heavy-tailed Laplace forecast-error increments. Trajectories of specific variables are integrated via PC-score matching to construct joint scenarios preserving inter-variable dependencies. A dense optimal response derived from these scenarios is compressed into a market-compatible 11-point bidding curve using FCP, which strategically allocates submission points to highly probable clearing intervals. Evaluation on 2021 NYISO West data demonstrates substantial improvements in both feasibility of scenarios and financial performance. The Laplace specification captures extreme price spikes, so it significantly reduces downside risk compared to a Gaussian baseline. PC-score matching ensures feasibility of structure by preserving daily trajectory shapes. Leveraging these robust scenarios, the FCP curve yields substantially higher realized settlements than the Uniform Support Baseline (USB), which uniformly places the limited submission points across the price range, recovering approximately 90% of the settlement gap between USB and the Dense Optimal Response (DOR), which serves as a non-submittable dense-grid upper-bound benchmark. Ultimately, this framework translates complex uncertainty models into actionable strategies, enabling producers to systematically maximize economic returns under rigid market constraints. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
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26 pages, 1019 KB  
Article
Do Increases and Decreases Matter Equally? Asymmetric and Regionally Heterogeneous Housing-Stock Interactions in Mainland China
by Mingyang Li, Woraphon Yamaka and Paravee Maneejuk
Mathematics 2026, 14(15), 2814; https://doi.org/10.3390/math14152814 - 5 Aug 2026
Viewed by 237
Abstract
This study examines the asymmetric relationship between housing prices and stock market returns across China’s major economic regions. Specifically, it investigates whether positive and negative shocks exhibit different transmission dynamics and whether these dynamics vary across regions characterized by different levels of financial [...] Read more.
This study examines the asymmetric relationship between housing prices and stock market returns across China’s major economic regions. Specifically, it investigates whether positive and negative shocks exhibit different transmission dynamics and whether these dynamics vary across regions characterized by different levels of financial development and housing market maturity. Using monthly data from 2005 to 2024, the study employs region-specific asymmetric vector autoregression (VAR) models, asymmetric Granger causality tests, and generalized impulse response analysis based on asymmetric decompositions of housing prices and stock market returns. The results suggest that statistically significant housing-to-stock predictability is observed primarily following negative housing price shocks in selected regions, whereas positive shocks generally exhibit weaker or statistically insignificant predictive effects. Conversely, positive stock market shocks generally provide more consistent evidence of stock-to-housing predictability, particularly in the Eastern and Central regions, although the responses are more mixed in the Western region and vary in magnitude, statistical significance, and persistence across regional markets. Overall, the results provide evidence of heterogeneous dynamic transmission patterns across China’s major economic regions and suggest that housing-related downside risk may represent an important source of regional macro-financial vulnerability. Full article
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41 pages, 5481 KB  
Article
Stochastic Risk-Aware Time–Cost Optimization of Construction Schedules Using a Hybrid GA–GWO Algorithm with Integer Crash-Day Decisions
by Mohammad Azimi Vaziri, Ali Erhan Öztemir and Salahi Pehlivan
Buildings 2026, 16(15), 3091; https://doi.org/10.3390/buildings16153091 - 4 Aug 2026
Viewed by 283
Abstract
Construction schedule compression requires balancing project-duration reduction against direct, indirect, and risk-related cost increases under uncertain activity performance. Many construction time–cost trade-off models still rely on deterministic durations or predefined execution modes, which limits their ability to represent practical activity-level crashing decisions under [...] Read more.
Construction schedule compression requires balancing project-duration reduction against direct, indirect, and risk-related cost increases under uncertain activity performance. Many construction time–cost trade-off models still rely on deterministic durations or predefined execution modes, which limits their ability to represent practical activity-level crashing decisions under uncertainty. This study develops a stochastic risk-aware time–cost optimization framework for construction scheduling using bounded integer crash-day decision variables. Activity durations are represented using triangular distributions based on optimistic, most-likely, and pessimistic estimates, while Monte Carlo simulation is used to propagate uncertainty through the precedence network. Expected and Conditional Value-at-Risk-oriented indicators are integrated into risk-adjusted duration and cost measures, which are then combined through a nonlinear normalized objective function. A Hybrid Genetic Algorithm–Gray Wolf Optimizer is implemented to solve the resulting discrete stochastic optimization problem and is benchmarked against seven metaheuristic algorithms under identical evaluation conditions. The framework is demonstrated using a 30-activity construction project reconstructed from Microsoft Project data. The proposed Hybrid GA–GWO reduced the deterministic project duration from 895 to 699 working days and achieved the best descriptive objective performance across 30 independent runs. However, after Bonferroni correction, its differences from the Genetic Algorithm and MPGWO-DLL were not statistically significant, indicating that these methods remain competitive alternatives. Additional Monte Carlo convergence, tornado sensitivity, correlated-duration sensitivity, and computational-time analyses were added to evaluate the stability, parameter dependence, and practical applicability of the framework. The findings show that the proposed framework can support risk-aware construction schedule-crashing decisions by identifying activity-level acceleration plans while explicitly accounting for downside schedule and cost risk. Broader validation in larger and more diverse real-world projects remains necessary. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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17 pages, 370 KB  
Article
An Adjustable Robust Approach for ESG-Aware Portfolio Optimization Under Decision-Dependent Return Uncertainty
by Futi Liu and Zian Zhao
Mathematics 2026, 14(15), 2793; https://doi.org/10.3390/math14152793 - 4 Aug 2026
Viewed by 182
Abstract
Portfolio optimization is a fundamental problem in financial decision-making, and it is concerned with balancing expected return and investment risk. With the growing emphasis on sustainable investing, environmental, social, and governance (ESG) criteria have been incorporated into portfolio optimization. In practice, ESG-aware portfolio [...] Read more.
Portfolio optimization is a fundamental problem in financial decision-making, and it is concerned with balancing expected return and investment risk. With the growing emphasis on sustainable investing, environmental, social, and governance (ESG) criteria have been incorporated into portfolio optimization. In practice, ESG-aware portfolio optimization faces parameter ambiguity from market fluctuations, delayed ESG disclosure, and rating disagreement, and the exposure to return uncertainty may depend on portfolio decisions rather than being fully exogenous. Existing studies, however, generally specify uncertainty sets independently of portfolio decisions. To address this limitation, an adjustable robust approach is proposed for ESG-aware portfolio optimization under decision-dependent return uncertainty. A joint polyhedral uncertainty set is constructed to capture the ambiguity in asset returns and ESG scores, where the return bounds depend on first-stage portfolio weights through ESG-related holdings, whereas ESG score uncertainty remains decision-independent. A two-stage robust framework with recourse rebalancing and proportional transaction costs is formulated, with financial loss and ESG performance balanced in the objective and tail risk controlled by a CVaR constraint embedded in a column-and-constraint generation scheme. The resulting minimax problem is solved by a column-and-constraint generation algorithm with a Rockafellar–Uryasev linearization of CVaR over iteratively generated scenarios. Numerical experiments using real stock data are designed to evaluate downside-risk control and portfolio ESG performance relative to deterministic and classical robust benchmarks. Full article
(This article belongs to the Section E5: Financial Mathematics)
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18 pages, 1921 KB  
Article
Levelized Cost of Electricity (LCOE) Assessment of Bifacial PV Systems in Uribia, Colombia: Integrating Stochastic Simulation and Machine Learning Under Fiscal Incentives
by Yimy Garcia Vera, Jaime Pérez and Edwin Villarreal-López
Energies 2026, 19(15), 3576; https://doi.org/10.3390/en19153576 - 30 Jul 2026
Viewed by 344
Abstract
This study evaluates the techno-economic viability of bifacial photovoltaic (PV) systems in Uribia, La Guajira—the department that holds Colombia’s strongest solar resource, with a mean global horizontal irradiance near 5.6 kWh/m2/day and seasonal peaks above 6.0. Despite this endowment, the country’s [...] Read more.
This study evaluates the techno-economic viability of bifacial photovoltaic (PV) systems in Uribia, La Guajira—the department that holds Colombia’s strongest solar resource, with a mean global horizontal irradiance near 5.6 kWh/m2/day and seasonal peaks above 6.0. Despite this endowment, the country’s installed solar capacity remains far below its potential, largely because developers lack the site-specific financial risk analyses that investment decisions require. To address this, we pair stochastic Monte Carlo simulation with a set of machine learning surrogate models and quantify how Colombia’s Law 1715 fiscal incentives—VAT exclusion and accelerated depreciation—reshape the Levelized Cost of Electricity (LCOE) of bifacial PV systems under realistic climatic variability. Drawing on six years of daily meteorological data, we model bifacial PERC performance under two ground-albedo conditions: the natural site value (α=0.125) and an optimized surface (α=0.30). The results are consistent and encouraging. Under the Law 1715 tax shields, the mean LCOE settles at 0.0588 USD/kWh, and even the 95% Value-at-Risk (VaR) of 0.0638 USD/kWh stays below the prevailing Colombian industrial tariff across every climatic realization evaluated—evidence that the fiscal framework does as much to compress downside risk as it does to lower the average cost. Ground-albedo optimization proved to be the decisive lever: raising α from 0.125 to 0.30 through low-cost surface preparation shortens the payback period to roughly four years and lets the bifacial configuration overtake the cumulative net present value of the monofacial baseline before year seven. The surrogate models tell a complementary story about the structure of the problem. The non-linear algorithms—Support Vector Regression, Gradient Boosting, a Multi-Layer Perceptron and Gaussian Process Regression—reproduce the Monte Carlo response surface almost exactly (R20.99, 0.994–0.997), whereas linear models trail at R20.900.94, a gap that quantifies just how strongly the techno-economic drivers of LCOE interact. Full article
(This article belongs to the Collection Featured Papers in Solar Energy and Photovoltaic Systems Section)
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29 pages, 2626 KB  
Article
Risk-Averse Co-Bidding of Hybrid Pumped-Hydro and Compressed-Air Long-Duration Energy Storage Under Shared Grid-Connection Constraints
by Jingyu Li, Junyu Zhang and Ruyue Han
Energies 2026, 19(15), 3562; https://doi.org/10.3390/en19153562 - 29 Jul 2026
Viewed by 260
Abstract
High penetrations of renewable generation are increasing the need for long-duration energy storage capable of intertemporal balancing and reserve provision. However, the market value of heterogeneous storage portfolios under shared grid-connection constraints remains insufficiently quantified. This study develops a risk-averse day-ahead co-bidding model [...] Read more.
High penetrations of renewable generation are increasing the need for long-duration energy storage capable of intertemporal balancing and reserve provision. However, the market value of heterogeneous storage portfolios under shared grid-connection constraints remains insufficiently quantified. This study develops a risk-averse day-ahead co-bidding model for a hybrid pumped-hydro and compressed-air energy storage (CAES) portfolio participating jointly in energy and spinning-reserve markets. Monte Carlo sampling and scenario reduction are used to represent price uncertainty, while conditional value-at-risk (CVaR) captures downside-profit risk. Shared point-of-common-coupling (PCC) constraints explicitly couple electricity sales, purchases, and reserve offers. Compared with homogeneous pumped-hydro expansion, replacing the equivalent incremental pumped-hydro capacity with CAES increases the cumulative reserve bid by 65.71%, while expected profit decreases by 1.17% and raw-scenario back-test CVaR remains nearly unchanged, decreasing by only 0.05%. Relative to the unconstrained hybrid-storage case, the shared PCC constraints reduce expected profit, raw-scenario back-test CVaR, and reserve bids by 1.01%, 1.34%, and 18.62%, respectively. Scenario-reduction sensitivity and synthetic price–spread analyses indicate that the main operating mechanisms remain stable within the assumed scenario-generation framework, while sensitivity analyses reveal diminishing returns from CAES expansion and saturation of PCC-related profit gains near 5000 MW. Because all price scenarios are synthetic and neither historical nor independent out-of-sample market data are used, these analyses constitute model-based robustness tests rather than seasonal or real-market validation. The findings support the coordinated configuration of heterogeneous storage, grid-interface capacity, and risk preferences, but should be interpreted as market-bidding-level comparative evidence under the adopted equivalent CAES representation rather than as market-specific profitability forecasts. Full article
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27 pages, 5112 KB  
Article
Dynamic Network Connectedness and Risk Spillovers Among DeFi, AI-Based, Islamic and Commodity Assets
by Lumengo Bonga-Bonga and Bereket Abayneh Ataro
J. Risk Financ. Manag. 2026, 19(8), 561; https://doi.org/10.3390/jrfm19080561 - 28 Jul 2026
Viewed by 424
Abstract
Against the backdrop of rapid technological innovation and the growing use of alternative investment instruments, this study examines the dynamic connectedness among decentralized finance assets, AI-based stocks, Islamic stocks and commodities. Covering the period from December 2019 to June 2022, we use the [...] Read more.
Against the backdrop of rapid technological innovation and the growing use of alternative investment instruments, this study examines the dynamic connectedness among decentralized finance assets, AI-based stocks, Islamic stocks and commodities. Covering the period from December 2019 to June 2022, we use the time-varying parameter vector autoregression (TVP-VAR) model to measure the magnitude, direction and evolution of return spillovers across Chainlink, Maker, Basic Attention Token, NVIDIA, Amazon, Google, Microsoft, DJIM World, DJIM EM, gold, crude oil and Global X Lithium and Battery Tech. The connectedness literature has examined spillovers across different asset classes during crisis periods. However, much of this literature focuses mainly on pairwise relationships among traditional asset classes, with limited attention to how emerging, alternative and technology-driven assets interact within a single network. We further assess the role of investor sentiment and network topology in identifying systemic transmitters and receivers. The results show strong interconnectedness, with an average total connectedness index (TCI) of 68.81%. Notably, AI-based stocks, especially Microsoft and NVIDIA, consistently emerge as net transmitters of return shocks, while commodities like gold and crude oil serve as absorbers of shocks. The portfolio results show that network centrality improves risk-adjusted performance by reducing volatility and downside risk. These insights have practical implications for policymakers and market participants, offering guidance for developing effective regulatory frameworks, investment strategies and risk management approaches in an increasingly interconnected financial landscape. Full article
(This article belongs to the Section Applied Economics and Finance)
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33 pages, 5699 KB  
Article
Research on Risk Spillovers and Early Warning Between Geopolitical Risk and China’s Financial Markets: A Quantile Time-Frequency Connectedness and Machine Learning Approach
by Baoshuai Zhang, Jinwei Zhang and Jun Duan
Int. J. Financ. Stud. 2026, 14(8), 195; https://doi.org/10.3390/ijfs14080195 - 24 Jul 2026
Viewed by 355
Abstract
Against the backdrop of rising geopolitical uncertainty, this paper uses daily data from 2013 to 2025 on the geopolitical risk index and China’s stock, bond, money, foreign exchange, commodity, gold, and real estate markets to construct a “quantile time-frequency connectedness–machine learning early warning” [...] Read more.
Against the backdrop of rising geopolitical uncertainty, this paper uses daily data from 2013 to 2025 on the geopolitical risk index and China’s stock, bond, money, foreign exchange, commodity, gold, and real estate markets to construct a “quantile time-frequency connectedness–machine learning early warning” framework. It examines the state-dependent characteristics of risk spillovers between changes in geopolitical risk and China’s financial markets, as well as the ability to identify high-risk states. The results show that, first, financial market risk connectedness exhibits a pronounced tail amplification effect: the total connectedness index is 13.72% under normal conditions, but rises to 77.97% and 78.47% under extreme downside and extreme upside states, respectively. Second, risk connectedness is mainly concentrated in the short term, although long-term connectedness strengthens under extreme states. Third, the stock, real estate, and commodity markets generally act as net transmitters of risk, while the bond and foreign exchange markets generally act as net receivers. Fourth, machine learning models based on dynamic connectedness indicators can effectively identify future high-risk connectedness states. However, naïve benchmarks and ablation tests indicate that the total connectedness index and its distance from the rolling threshold are the main sources of information, while the contribution of machine learning models lies mainly in probability calibration, multi-horizon risk ranking, and the integration of auxiliary variables. The findings provide empirical evidence for cross-market risk monitoring and the construction of early warning indicators under geopolitical risk. Full article
(This article belongs to the Special Issue Financial Markets in China: AI Applications, AI Risk and Governance)
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33 pages, 11472 KB  
Article
Stochastic Bi-Level Optimization of Pavement Rehabilitation and Toll Pricing Under Demand Feedback in Toll-Road Corridors
by Honggang Wang, Ye Li, Baozhen Jiang and Haozhe Zhu
Appl. Sci. 2026, 16(15), 7401; https://doi.org/10.3390/app16157401 - 23 Jul 2026
Viewed by 270
Abstract
Toll-road operators must coordinate pavement rehabilitation and toll pricing because surface condition and tolls jointly affect route choice, realized demand, deterioration, and long-term revenue. Motivated by infrastructure REIT asset-operation requirements, this study develops a stochastic bi-level multi-period model for joint pavement maintenance and [...] Read more.
Toll-road operators must coordinate pavement rehabilitation and toll pricing because surface condition and tolls jointly affect route choice, realized demand, deterioration, and long-term revenue. Motivated by infrastructure REIT asset-operation requirements, this study develops a stochastic bi-level multi-period model for joint pavement maintenance and toll pricing under demand feedback. The upper level selects annual tolls and rehabilitation intensities for tolled links subject to budget and service constraints. The lower level solves an elastic-demand user equilibrium based on generalized travel disutility. The operator objective extends discounted-profit maximization by adding revenue coefficient of variation, maximum drawdown, and terminal pavement value. Budget availability and deterioration uncertainty are represented by scenario multipliers, and the model is solved by a real-coded genetic algorithm coupled with the method of successive averages (GA-MSA). Experiments on the Li-Sheng benchmark and a semi-empirical Nanjing toll-road REIT corridor show that stochastic coordinated decisions retain more than 97% of the NPV achieved by the GA-MSA profit-oriented benchmark while improving revenue stability and limiting downside risk. Supplementary comparisons with PSO-MSA and DE-MSA show that alternative upper-level search rules identify different points on the normalized risk–return surface. The findings support treating maintenance and pricing as an integrated asset-operation problem for long-horizon toll-road assets. Full article
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35 pages, 4737 KB  
Article
Climate Risk Contagion and Financial Stability During the Low-Carbon Transition: A Multiscale Vine-Copula Analysis
by Li Zeng and Jinghui Huang
Sustainability 2026, 18(14), 7344; https://doi.org/10.3390/su18147344 - 17 Jul 2026
Viewed by 351
Abstract
As the global economy accelerates toward low-carbon transformation, climate financial risks are emerging as a key challenge to monetary policy design and financial stability oversight. This study examines the contagion effects and dynamic interdependencies among domestic climate-sensitive industries, financial climate risk indices, and [...] Read more.
As the global economy accelerates toward low-carbon transformation, climate financial risks are emerging as a key challenge to monetary policy design and financial stability oversight. This study examines the contagion effects and dynamic interdependencies among domestic climate-sensitive industries, financial climate risk indices, and international climate markets. Using daily data from April 2020 to April 2025, we apply a multiscale tail risk modeling framework that integrates wavelet decomposition, conditional volatility modeling, and vine-copula techniques to capture time-varying and asymmetric dependence structures across markets. The results show that the three markets display volatility clustering, fat tails, and nonlinear dependence. The international climate market shows weaker and more volatile connections with the two domestic markets, suggesting that external climate expectations operate mainly through indirect dependence across market states. The risk spillover results further show that climate financial risk contagion differs between upside and downside states and varies across short and medium horizons. These findings have important implications for integrating climate risk into macroprudential surveillance. Central banks and regulators should strengthen early warning mechanisms, climate stress testing, and scenario analysis by considering market-specific, nonlinear, and multiscale risk spillovers. The main contribution of this study is to integrate multiscale decomposition, conditional volatility modelling, and vine-copula dependence analysis into a unified empirical framework for identifying climate financial risk contagion across markets. The findings offer useful evidence for climate stress testing, early warning systems, and financial stability monitoring in emerging markets. Full article
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19 pages, 19765 KB  
Article
Joint Effects of Price and Generation-Forecast Errors on Offshore Wind Revenue and Downside Risk Under Dual Settlement: Evidence from Guangdong, China
by Shujun Lou, Youchao Zheng, Shuyi Chen, Peilin Wu, Chao Liu and Zhan Lian
Energies 2026, 19(14), 3370; https://doi.org/10.3390/en19143370 - 16 Jul 2026
Viewed by 288
Abstract
China’s power sector is accelerating its transition to spot-market clearing with increasing offshore wind penetration. This transition poses compounded operational and economic challenges, as the interaction between generation variability and price volatility affects both producer revenues and real-time system balancing costs. This study [...] Read more.
China’s power sector is accelerating its transition to spot-market clearing with increasing offshore wind penetration. This transition poses compounded operational and economic challenges, as the interaction between generation variability and price volatility affects both producer revenues and real-time system balancing costs. This study utilizes full-year hourly generation and spot price data from an offshore wind farm in eastern Guangdong, which represents the largest offshore wind industry cluster and a premier high-wind-resource area along China’s near-sea coasts. This empirical dataset provides significant value for characterizing real-world market behaviors under Guangdong’s dual-settlement framework. By employing a settlement-consistent Monte Carlo framework to quantify the joint effects of forecast errors, our results reveal that while downside risk is primarily driven by generation volume errors under normal conditions, the negative correlation between wind output and prices intensifies revenue volatility. Furthermore, under high-stress scenarios characterized by extreme market volatility and large deviations, price uncertainty emerges as the dominant driver of tail risk. Ultimately, these findings demonstrate that probabilistic forecasting for both prices and generation is essential not only for producer risk management but also for supporting dispatchable decision-making and reliable operation of power systems with high shares of renewable energy. Full article
(This article belongs to the Section A: Sustainable Energy)
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39 pages, 14379 KB  
Article
Distribution-Robust Graph Representation Learning for Portfolio Optimization
by Ziteng Meng, Bo Ma, Yiqi Zhang, Aiqi Yang and Yifan Li
Mathematics 2026, 14(14), 2468; https://doi.org/10.3390/math14142468 - 8 Jul 2026
Viewed by 468
Abstract
Multi-asset portfolio optimization under non-stationary financial markets requires robust state representations across market phase transitions. This paper proposes distribution-robust graph representation learning for portfolio optimization (DR-GRL-PO), which learns asset-dependency graph representations as robust cross-asset structural priors for policy learning. DR-GRL-PO consists of a [...] Read more.
Multi-asset portfolio optimization under non-stationary financial markets requires robust state representations across market phase transitions. This paper proposes distribution-robust graph representation learning for portfolio optimization (DR-GRL-PO), which learns asset-dependency graph representations as robust cross-asset structural priors for policy learning. DR-GRL-PO consists of a market-phase invariant graph contrastive encoding module (MPIGCE), a distribution-robust predictive coding module (DRPC), and a portfolio policy learning module (PPL). MPIGCE learns invariant structural priors from Spearman-based asset-dependency graphs, DRPC incorporates these priors into dual-scale predictive branches with invariant ranking consistency, and PPL integrates structural priors and predictive states for dynamic asset allocation. The model is evaluated on three separate datasets for portfolio construction, using daily data from CSI-300 (2011–2021), NASDAQ-100 (2011–2021), and Cryptocurrency (2017–2026) markets. The results show that DR-GRL-PO mainly improves wealth growth, annualized profitability, and risk-adjusted performance, while maintaining a certain degree of downside-risk control and a favorable upside–downside return balance. Its performance across separate market categories and market phases provides evidence of robustness under non-stationary market conditions. These findings indicate that robust cross-asset structural priors can support more reliable dynamic portfolio allocation. Full article
(This article belongs to the Special Issue Portfolio Optimization and Risk Management In Financial Markets )
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27 pages, 5302 KB  
Article
Decision-Centric Portfolio Selection for Sustainable Supply Chain Risk Management: A Simulation-Optimization Framework for Robust Decision Support
by Kilhwan Kim, Sungjune Park and Ram L. Kumar
Sustainability 2026, 18(13), 6863; https://doi.org/10.3390/su18136863 - 6 Jul 2026
Viewed by 245
Abstract
Sustainable supply chains are increasingly vulnerable to systemic risks, such as geopolitical conflicts at critical trade routes like the Strait of Hormuz or climate disasters, which reveal deep Environmental, Social, and Governance (ESG) weaknesses. Conventional optimization often fails in these “deep uncertainty” contexts, [...] Read more.
Sustainable supply chains are increasingly vulnerable to systemic risks, such as geopolitical conflicts at critical trade routes like the Strait of Hormuz or climate disasters, which reveal deep Environmental, Social, and Governance (ESG) weaknesses. Conventional optimization often fails in these “deep uncertainty” contexts, where reliable historical data are often scarce and qualitative factors are paramount. This study introduces a simulation-optimization framework that reframes risk management as a decision process rather than a purely computational one. Portfolios are parameterized across five key characteristics—prevention, vulnerability, resilience, recovery, and detection—to enable a genetic algorithm (GA) to generate a diverse ensemble of high-performing strategies. Instead of providing one “best” answer, the GA allows managers to evaluate multiple options against quantitative tail-risk measures and qualitative institutional factors. The framework produces a “trade-off map,” or Pareto frontier, visualizing the cost of protecting against downside risks. By adjusting the GA’s settings, decision makers can toggle between improving current plans and exploring new, structurally different strategies. The numerical results demonstrate that the GA consistently identifies high-performing portfolios, achieving at least 99.55% of the true optimal performance across all metrics while requiring only 25% of the computational evaluation budget of an exhaustive search space. Furthermore, the framework successfully generates a structurally diverse menu of near-optimal alternatives across all performance metrics, consistently outperforming Monte Carlo sampling in the quality of near-optimal solutions identified, particularly for tail-risk measures such as conditional value-at-risk. Ultimately, this approach integrates the manager’s professional judgment regarding non-quantifiable factors, such as political stability and social responsibility, with simulation data to support the selection of a robust, sustainable portfolio. Full article
(This article belongs to the Section Sustainable Management)
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26 pages, 11719 KB  
Article
Multi-Level Spatial Design Decision-Making Model for Block Caving Systems in Super-Large Open-Pit Mines
by Qi-Ang Wang, Gao-Yu Cui, Guo-Quan Sun, Bei-Dou Ding, Zhan-Guo Ma, Jia-Mian Yang, Peng Gong, Ji Liu and Hao-Yu Zhu
Appl. Sci. 2026, 16(13), 6753; https://doi.org/10.3390/app16136753 - 6 Jul 2026
Viewed by 304
Abstract
As global super-large open-pit mines expand in scale and extraction depth, conventional single-stage planning cannot meet the combined demands of productivity and resource recovery, making the shift to underground block caving inevitable. This study outlines the systemic challenges of block-scale extraction and the [...] Read more.
As global super-large open-pit mines expand in scale and extraction depth, conventional single-stage planning cannot meet the combined demands of productivity and resource recovery, making the shift to underground block caving inevitable. This study outlines the systemic challenges of block-scale extraction and the rationale for adopting multi-level spatial design decision-making. Four core model categories are briefly proposed: ultimate pit limit optimization, gravity flow simulation for draw strategy, long-term production scheduling for large-scale computation, and probabilistic frameworks addressing geological and market uncertainty. A Bayesian network-based block decision model is then proposed and decoupled into three physical decision tiers. The first tier incorporates energy prices, transport costs, and ore prices to establish an economic boundary rating robust to market volatility. The second tier aggregates mining units with discrete-event perturbations to produce a reliability-oriented production rating. The third tier integrates rock mechanics parameters with in situ monitoring data to derive a physics-informed safety rating. The three ratings are synthesized via Bayesian inference and evaluated within a multi-attribute utility function encompassing net present value, safety index, downside risk, and information risk. A feedback module quantifies the economic benefit of uncertainty reduction, yielding a closed-loop intelligent system spanning macroeconomic boundary definition to operational safety alerting. Finally, the main conclusion of this study is that integrating macro-economic volatility with rock mechanics through a dynamic Bayesian framework is essential for managing the open-pit to underground transition. The results indicate that leveraging the Value of Information for real-time risk diagnosis significantly reduces conservative design losses, providing a quantifiable and robust decision-making paradigm for super-large mining systems. Full article
(This article belongs to the Special Issue Engineering Structure Risk Assessment and Decision-Making Support)
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