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Search Results (448)

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Keywords = stochastic volatility

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29 pages, 3525 KB  
Article
An Intelligent Computing Architecture for Ultra-Short-Term Wind Power Forecasting: Integrating Dual-Stage Signal Processing and Optimized Deep Learning
by Yuting Zhang and Xiaonan Shen
Inventions 2026, 11(3), 61; https://doi.org/10.3390/inventions11030061 - 16 Jun 2026
Viewed by 98
Abstract
The integration of wind energy into power systems relies on forecasting technologies to address operational challenges caused by its volatility and intermittency. This paper proposes a computing architecture for ultra-short-term wind power forecasting. The methodology integrates an adaptive dual-stage signal processing technique with [...] Read more.
The integration of wind energy into power systems relies on forecasting technologies to address operational challenges caused by its volatility and intermittency. This paper proposes a computing architecture for ultra-short-term wind power forecasting. The methodology integrates an adaptive dual-stage signal processing technique with an optimized deep learning model. To manage the non-stationarity of meteorological variables, the Pearson and Maximal Information Coefficient (MIC) analyses are employed for feature selection. The ICEEMDAN algorithm is then used for initial decomposition, followed by sample entropy and K-Means clustering to assess component complexity. Variational Mode Decomposition (VMD) is applied only to the high-frequency component to further separate stochastic fluctuations while preserving relatively stable trend components. A Convolutional Neural Network-Bidirectional Long Short-Term Memory (CNN-BiLSTM) network is constructed to forecast the resulting multi-scale components. To reduce reliance on manual empirical tuning, the Crested Porcupine Optimizer (CPO) is used to fine-tune key network hyperparameters. Evaluations using operational wind-farm data indicate that the developed hybrid method captures the temporal dynamics of wind power and yields lower prediction errors than the tested benchmark models. This research provides a data-driven computing framework for renewable-energy forecasting and related operational analysis. Full article
20 pages, 4695 KB  
Review
Dual-Mechanism Synergistic Regulation and Performance Optimization of Lead Sulfide Quantum Dot Coatings in Optoelectronic Memristors
by Ru Li, Xinhe Jiang, Xuhao Zhao, Huiyun Zhang, Qingyu Xu and Guangyu Wang
Coatings 2026, 16(6), 715; https://doi.org/10.3390/coatings16060715 - 15 Jun 2026
Viewed by 282
Abstract
Lead sulfide quantum dots (PbS QDs), as a functional-layer coating, enable non-volatile integration and neuromorphic computing in memristive structures to address the von Neumann bottleneck. Herein, the dual-interface mechanism of PbS QDs in the memristor film structure is reviewed. First, the local electric [...] Read more.
Lead sulfide quantum dots (PbS QDs), as a functional-layer coating, enable non-volatile integration and neuromorphic computing in memristive structures to address the von Neumann bottleneck. Herein, the dual-interface mechanism of PbS QDs in the memristor film structure is reviewed. First, the local electric field enhancement effect generates tip electrode-like structures in the coating film through QD-mediated spatial charge gradients, thereby enabling precise control over the nucleation and growth of conductive filaments (CFs). As a result, the consistency of switching voltages and the thermal stability at elevated temperatures are significantly improved. Conversely, the anion reservoir effect exploits surface dangling bonds on QDs to efficiently capture anions from the dielectric layer, thereby synergistically regulating vacancy migration kinetics. This process enables zero-initialization behavior and ultra-low-power operation. In addition, the spatial distribution design and density modulation of QDs further reinforce both mechanisms. The structural optimization of QD/dielectric interface engineering can simultaneously improve cycling endurance and resistive switching uniformity. Furthermore, modification of QD surface chemistry through ligand decoration and passivation suppresses the stochasticity of ionic diffusion while improving the linearity of synaptic weight updates. This interfacial engineering strategy utilizing QDs as coating films advances the development of high-performance photonic–electronic systems for memory–computing convergence. Full article
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60 pages, 10824 KB  
Article
Forecasting South Africa’s Coal-to-Clean Energy Transition: A Monte Carlo Simulation
by Luyanda Majenge, Simiso Msomi and Sakhile Mpungose
Forecasting 2026, 8(3), 47; https://doi.org/10.3390/forecast8030047 - 12 Jun 2026
Viewed by 316
Abstract
South Africa remains one of the world’s most coal-dependent electricity systems, with coal accounting for 81.57% of generation in 2023. Despite policy interventions to diversify the energy mix, structural change is slow to emerge. This study provides the first integrated, empirically calibrated forecast [...] Read more.
South Africa remains one of the world’s most coal-dependent electricity systems, with coal accounting for 81.57% of generation in 2023. Despite policy interventions to diversify the energy mix, structural change is slow to emerge. This study provides the first integrated, empirically calibrated forecast of South Africa’s coal-to-clean-energy transition using a unified modelling architecture that combines structural break analysis, Bayesian estimation, and an enhanced Monte Carlo simulation with dynamic volatility (10,000 stochastic pathways). The findings confirm a permanent structural break in 2011 that coincided with the implementation of REIPPPP, following which coal began a statistically significant and sustained decline of approximately 0.7–0.75% points per year. The simulation produced a full probability distribution for the transition year (2053) when coal share falls below 50%. This demonstrated that long-term uncertainty rises faster than linearly and that, under current conditions, deep decarbonisation milestones are unattainable before mid-century. Policy scenario experiments also demonstrated that accelerating the annual decline rate necessitates coordinated, synergistic policy portfolios rather than isolated interventions. These findings provide a transparent, uncertainty-explicit forecast of South Africa’s transition trajectory, as well as a decision-relevant evidence base for planning, regulation, and equitable transition implementation. Full article
(This article belongs to the Section Power and Energy Forecasting)
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36 pages, 1574 KB  
Article
A Unified Longevity–Financial Risk Framework for Evaluating Pension Funding Ratios
by Francesco Rania
Risks 2026, 14(6), 130; https://doi.org/10.3390/risks14060130 - 10 Jun 2026
Viewed by 130
Abstract
Defined-benefit pension funds face simultaneous exposure to longevity risk and financial market volatility, yet most regulatory frameworks assess these risks in isolation using deterministic methods. This paper examines how their joint occurrence affects fund solvency measured by the funding ratio. We develop an [...] Read more.
Defined-benefit pension funds face simultaneous exposure to longevity risk and financial market volatility, yet most regulatory frameworks assess these risks in isolation using deterministic methods. This paper examines how their joint occurrence affects fund solvency measured by the funding ratio. We develop an integrated stochastic framework combining a generalized Lee–Carter model with cohort effects for mortality, a two-state Markov regime-switching process for asset returns, and a Cox–Ingersoll–Ross model for stochastic interest rates; liabilities are valued under the risk-neutral measure. The model is calibrated to Italian ISTAT/HMD mortality data and institutional benchmarks over 2000–2023; solvency risk is quantified via value-at-risk and conditional value-at-risk of the funding ratio at one-, five-, and ten-year horizons (M=50,000 Monte Carlo scenarios). Financial risk dominates at the one-year horizon (CVaR0.99=59.1 percentage points), while longevity risk grows from 4% of the total tail risk at one year to 21% at ten years. The stochastic VaR0.99 exceeds deterministic reserves by a factor of 4.8×, and the standard modular aggregation formula overestimates combined risk by up to five percentage points due to its Gaussian copula assumption. These results demonstrate that integrated stochastic modeling is essential for sound regulatory capital assessment under the IORP II framework. Full article
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19 pages, 20213 KB  
Article
Broken Symmetry, “Conservation Law”, and Scaling in Accumulated Stock Returns: A Modified Jones–Faddy Skew t-Distribution Perspective
by Arshia Ghasemi, Siqi Shao and R. A. Serota
Foundations 2026, 6(2), 23; https://doi.org/10.3390/foundations6020023 - 9 Jun 2026
Viewed by 160
Abstract
We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably [...] Read more.
We analyze historic S&P500 multi-day returns: from daily returns to those accumulated over up to ten days. Despite symmetry breaking between gains and losses in the distribution of returns, resulting in its positive mean and negative skew, realized variance (volatility squared) exhibits remarkably good linear dependence on the number of days of accumulation. Mean of the distribution also shows near perfect linear dependence as well. We analyze this phenomenon both analytically and numerically using a modified Jones–Faddy skew t-distribution. Full article
(This article belongs to the Section Mathematical Sciences)
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25 pages, 1473 KB  
Article
From Heuristics to Reinforcement Learning: Integrated Operational–Financial Control of Supply Chains Under Demand Disruption
by Ali Badakhshan, Ehsan Badakhshan, Sameh Saad and Ramin Bahadori
Appl. Sci. 2026, 16(11), 5712; https://doi.org/10.3390/app16115712 - 5 Jun 2026
Viewed by 168
Abstract
Supply chain control requires balancing operational performance and financial efficiency when decisions are made using delayed and imperfect demand information. Although fixed heuristics, adaptive policies, and reinforcement learning approaches have been proposed, their relative effectiveness and robustness under temporary informational mismatch remain unclear. [...] Read more.
Supply chain control requires balancing operational performance and financial efficiency when decisions are made using delayed and imperfect demand information. Although fixed heuristics, adaptive policies, and reinforcement learning approaches have been proposed, their relative effectiveness and robustness under temporary informational mismatch remain unclear. This study addresses this gap by developing an integrated simulation–reinforcement learning framework that jointly captures operational and financial dynamics in supply chains, which enables adaptive optimisation of working capital policies under uncertainty. A unified simulation framework is developed for a multi-echelon supply chain that jointly models service levels, backlog, customer retention, and working capital exposure through the cash conversion cycle. Five classes of controllers are evaluated: fixed-threshold heuristics, adaptive threshold policies optimised using stochastic and evolutionary search, and a reinforcement learning controller based on proximal policy optimisation. Performance is assessed under stationary demand and under demand disruptions. The results reveal a clear hierarchy of performance. Fixed heuristics provide transparent and stable baselines but suffer from structural rigidity. Adaptive threshold policies substantially improve coordination, with evolutionary search yielding the strongest performance among structured approaches. The reinforcement learning controller achieves the best overall outcomes by learning a nonlinear state–action mapping that sharply reduces backlog and service shortfalls while maintaining comparable working capital exposure. These gains arise from improved coordination across operational and financial decisions rather than single-metric optimisation. Practically, adaptive heuristics offer robust baselines, while learning-based controllers are most valuable in more volatile environments. Full article
(This article belongs to the Special Issue Novel Approaches for Future Supply Chains and Smart Logistics)
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29 pages, 2534 KB  
Article
Generative Adversarial Networks for Inpainting Implied Volatility Surfaces
by Taonga Leeroy Maoneni, Hermann Azemtsa Donfack and Celestin Wafo Soh
Mathematics 2026, 14(11), 1995; https://doi.org/10.3390/math14111995 - 4 Jun 2026
Viewed by 162
Abstract
Implied volatility surfaces describe option-implied volatilities across strikes, and maturities and play a central role in derivative pricing and risk management. However, in practice, they are often incomplete due to illiquidity or sparse trading, requiring reliable reconstruction of missing regions. Existing approaches typically [...] Read more.
Implied volatility surfaces describe option-implied volatilities across strikes, and maturities and play a central role in derivative pricing and risk management. However, in practice, they are often incomplete due to illiquidity or sparse trading, requiring reliable reconstruction of missing regions. Existing approaches typically rely on parametric assumptions or latent space optimisation methods, which may be restrictive or computationally intensive. This study proposes a data-driven framework based on conditional generative adversarial networks (GANs) to map partially observed surfaces to completed ones in a single forward pass. The approach is evaluated in a controlled setting using synthetic data generated from the Heston stochastic volatility model, with varying levels of missingness (10–96%). The generator objective incorporates penalty terms enforcing the absence of call-spread, butterfly-spread, and calendar-spread arbitrage, together with a smoothness regulariser on the implied risk-neutral density. Compared with a conditional variational autoencoder (VAE), the Bates model, and the stochastic volatility-inspired (SVI) parameterisation, the proposed approach achieves lower reconstruction errors across all levels of missingness, including unseen cases, while preserving the no-arbitrage properties. An ablation study shows that the conditional GAN implicitly learns no-arbitrage behaviour, with density smoothness regularisation being the only constraint that meaningfully improves reconstruction quality. Full article
(This article belongs to the Section E5: Financial Mathematics)
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25 pages, 338 KB  
Article
Scenario-Based Financial Planning in Gold Mining Under Commodity Price Uncertainty
by Lemonia Choupi, Vasilios Margaris and Georgios Angelidis
Commodities 2026, 5(2), 12; https://doi.org/10.3390/commodities5020012 - 4 Jun 2026
Viewed by 163
Abstract
Gold mining firms operate in an environment characterized by substantial commodity price volatility, capital intensity, and long investment horizons. Traditional deterministic financial planning frameworks are insufficient to capture the nonlinear and asymmetric risks associated with gold price fluctuations. This study develops a simulation-based [...] Read more.
Gold mining firms operate in an environment characterized by substantial commodity price volatility, capital intensity, and long investment horizons. Traditional deterministic financial planning frameworks are insufficient to capture the nonlinear and asymmetric risks associated with gold price fluctuations. This study develops a simulation-based scenario planning framework for gold mining firms, integrating deterministic scenario analysis with stochastic price modeling. Using a stylized and benchmark-calibrated financial model intended for methodological illustration rather than firm-specific forecasting, the study evaluates the impact of gold price uncertainty on key financial indicators, including EBITDA, free cash flow, and net present value. Monte Carlo simulations indicate substantial dispersion in financial outcomes, with approximately 28% of simulated realizations producing negative Net Present Value outcomes under baseline assumptions. The results further demonstrate that volatility significantly amplifies downside exposure despite positive expected returns, thereby highlighting the limitations of deterministic planning approaches. The findings suggest that probabilistic scenario-based financial planning provides a more comprehensive framework for evaluating financial resilience and tail-risk exposure in commodity-dependent industries. Full article
22 pages, 7997 KB  
Article
Automated Electrolyzer Control System for the Production, Accumulation, and Storage of Hydrogen for Refueling Vehicles
by Linfei Chen and Boichenko Sergii
Hydrogen 2026, 7(2), 76; https://doi.org/10.3390/hydrogen7020076 - 2 Jun 2026
Viewed by 302
Abstract
On-site hydrogen refueling stations (HRS) face significant operational challenges due to the stochastic nature of hydrogen demand, creating a severe supply–demand mismatch. Under traditional pressure-based hysteresis control, this volatility forces Proton Exchange Membrane (PEM) electrolyzers into frequent start–stop cycles, accelerating degradation and reducing [...] Read more.
On-site hydrogen refueling stations (HRS) face significant operational challenges due to the stochastic nature of hydrogen demand, creating a severe supply–demand mismatch. Under traditional pressure-based hysteresis control, this volatility forces Proton Exchange Membrane (PEM) electrolyzers into frequent start–stop cycles, accelerating degradation and reducing efficiency. In response, this study introduces an automated control framework integrating macroscopic gas-state modeling with deep-learning-based demand prediction. First, a real-gas thermodynamic model was established. Monte Carlo simulations of 100 random filling scenarios identified a robust design benchmark of 4.5 kg per vehicle. A low filling stability coefficient (5.02%) confirmed that individual thermodynamic fluctuations are negligible, validating a traffic-flow-driven demand approach. Next, a deep Long Short-Term Memory (LSTM) network was developed to forecast short-term demand. Trained on an 8784 h dataset exhibiting “double-peak” traffic patterns, the model achieved high precision on the unseen test set, yielding a Root Mean Square Error (RMSE) of 6.75 kg and a normalized RMSE (nRMSE) of 0.0987, explaining 82% of the demand variance. Finally, an LSTM-informed demand-following control strategy was formulated to enable proactive, thermally bounded operation alongside a novel “Hot Standby” mechanism. Maintaining a minimal 3.0 kg/h holding current during idle periods sustains stack temperatures above 60 °C, effectively mitigating thermal stress. Comparative simulations over 1464 h demonstrated that the proposed framework reduces detrimental cold start–stop cycles by 98.4% (from 61 to 1) and suppresses power output fluctuations by 40.7% compared to the traditional baseline. These results confirm that data-driven control significantly enhances operational stability, facilitates grid integration, and extends core equipment service life. Full article
(This article belongs to the Special Issue Green and Low-Emission Hydrogen: Pathways to a Sustainable Future)
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29 pages, 14977 KB  
Article
Why Is Offshore Gas-to-Wire with CCUS Geopolitically and Economically Critical to Decarbonization?
by Icaro B. Boa Morte, Israel Bernardo S. Poblete, Cláudia R. V. Morgado, José Luiz de Medeiros and Ofélia de Queiroz Fernandes Araújo
Processes 2026, 14(11), 1791; https://doi.org/10.3390/pr14111791 - 30 May 2026
Viewed by 334
Abstract
Carbon taxes and credits (CT&C) accelerate global deployment of carbon capture, utilization and storage (CCUS) technologies to enable energy transition. This study investigates the economic performance and resilience of floating gas-to-wire with CCUS (f-GTW-CCUS), deployed at the wellhead of stranded CO2-rich [...] Read more.
Carbon taxes and credits (CT&C) accelerate global deployment of carbon capture, utilization and storage (CCUS) technologies to enable energy transition. This study investigates the economic performance and resilience of floating gas-to-wire with CCUS (f-GTW-CCUS), deployed at the wellhead of stranded CO2-rich offshore oil and gas reservoirs. The f-GTW-CCUS platform integrates a natural gas combined cycle power plant with monoethanolamine post-combustion capture (PCC-MEA), producing low-carbon electricity (23 kgCO2e/MWh, competitive with renewables) while monetizing captured CO2 via enhanced oil recovery (EOR). The mass and energy balance data from the proposed process configuration were obtained in the literature. Critically, f-GTW-CCUS operates on wellhead-sourced in situ-associated gas, eliminating exposure to volatile natural gas markets, and achieves a levelized cost of electricity (LCOE) of USD 67.15/MWh. Monte Carlo analysis (10,000 Gaussian iterations, 30-year lifetime, 10% discount rate, three CT&C scenarios, namely, low/medium/high) is used to quantify economic feasibility across three stochastic variables: oil, natural gas, and electricity prices, starting in the 5th year. The results demonstrate the following: (1) Case A (f-GTW without CCUS) remains economically infeasible (NPV < 0) under all price volatility scenarios due to insufficient electricity-only revenue and carbon taxation penalties; (2) Case B (f-GTW-CCUS with immediate CCUS deployment) maintains positive NPV across all scenarios, with EOR monetization contributing 43% of total revenue; (3) the critical CCUS deployment-delay threshold is 6 years under high carbon taxation, extending to 10 years when carbon credits are included. Gate-to-gate environmental assessment (carbon intensity, water footprint, land transformation) shows f-GTW-CCUS superiority versus alternative power systems, with minimal water–land nexuses due to offshore desalination. An empirical consistency assessment based on the 2026 geopolitical energy crisis demonstrates the structural resilience of the f-GTW-CCUS plant: the wellhead sourcing provides resilience to global natural gas price shocks, while the concurrent crude price escalation amplifies EOR revenues by 43–57%, improving project feasibility during commodity disruptions. These findings position f-GTW-CCUS as a critical decarbonization pathway for O&G producers exploiting stranded gas reserves. The technology combines carbon intensity reduction with economic resilience under volatile energy market conditions and mandatory climate policies. Full article
(This article belongs to the Special Issue Oil and Gas Drilling Processes: Control and Optimization, 2nd Edition)
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32 pages, 2903 KB  
Article
A Goodness-of-Fit Framework for Assessing Distributional Symmetry and Tail Asymmetry in Financial Equity Markets
by Abdullah Sevin and Alpha Abdoulaye Bah
Symmetry 2026, 18(6), 943; https://doi.org/10.3390/sym18060943 - 30 May 2026
Viewed by 284
Abstract
The assumption that highly correlated financial assets share identical risk profiles often overlooks crucial distributional asymmetries. This study introduces a Goodness-of-Fit (GoF) framework to evaluate stochastic symmetry and structural alignment of equity returns. Moving beyond linear correlation, we apply non-parametric GoF tests—Kolmogorov–Smirnov, permutation-based [...] Read more.
The assumption that highly correlated financial assets share identical risk profiles often overlooks crucial distributional asymmetries. This study introduces a Goodness-of-Fit (GoF) framework to evaluate stochastic symmetry and structural alignment of equity returns. Moving beyond linear correlation, we apply non-parametric GoF tests—Kolmogorov–Smirnov, permutation-based Anderson–Darling, and Epps–Singleton—complemented by Energy Distance metrics, Extreme Value Theory (EVT) for 1% and 5% tail asymptotics, and robust L-moments to quantify tail asymmetry. We analyze major stocks against market indices and sectoral ETFs using ARMA-GARCH filtered innovations to isolate IID components. Our findings reveal a significant decoupling between correlation and stochastic symmetry; highly correlated assets frequently exhibit tail asymmetry and structural drift. Energy Distance decomposition isolates shape-driven deviations from scale-driven volatility. Furthermore, hierarchical clustering categorizes assets into distinct risk profiles, bridging structural divergence and left-tail risk. A 1000-iteration bootstrapped backtest shows that integrating our GoF framework with tail-risk penalties improves risk-adjusted performance, evidenced by superior Sharpe ratios (outperforming 80.3% of random allocations). In conclusion, high linear correlation does not guarantee distributional symmetry. The proposed framework offers deeper insights into asymmetric asset behavior than conventional second moment metrics, providing a robust tool for portfolio risk management under non-Gaussian market conditions. Full article
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23 pages, 2726 KB  
Article
Multi-Uncertainty Optimal Scheduling of Integrated Electricity and Heat Energy Systems Based on Fuzzy-IGDT
by Na Sun, Hongxu He, Yunyun Yun and Shuaibing Li
Processes 2026, 14(11), 1784; https://doi.org/10.3390/pr14111784 - 29 May 2026
Viewed by 224
Abstract
The presence of multiple uncertainties in integrated electricity–heat energy systems (E-HIES) poses significant challenges to system dispatch. To achieve an effective balance between economy and robustness, this paper proposes an optimal scheduling method based on fuzzy chance-constrained Information Gap Decision Theory (Fuzzy-IGDT), accounting [...] Read more.
The presence of multiple uncertainties in integrated electricity–heat energy systems (E-HIES) poses significant challenges to system dispatch. To achieve an effective balance between economy and robustness, this paper proposes an optimal scheduling method based on fuzzy chance-constrained Information Gap Decision Theory (Fuzzy-IGDT), accounting for uncertainties in wind power output, photovoltaic output, electrical load, and thermal load. The method employs trapezoidal fuzzy numbers to model the four types of uncertain variables and constructs a fuzzy robust model (F-RM) for conservative decision-makers and a fuzzy opportunity model (F-OM) for aggressive decision-makers. An Adaptive Step Ratio (ASR) optimization method is then developed to solve the proposed models. Case studies demonstrate the effectiveness of the proposed methodology. Results show that: compared with conventional IGDT, pure fuzzy and stochastic programming, Fuzzy-IGDT simultaneously optimizes economy, stability and reliability: daily operating cost is reduced by 12.7%, the standard deviation of cost volatility shrinks by 34.5%, and the loss-of-load probability is only 0.3%. Relative to the traditional Weighted Offset Coefficient (WOC) method, ASR directly coordinates the deviation ratios of multiple variables through its step-ratio mechanism, cutting system risk cost by 21.3%, raising solution efficiency by 42%, and improving convergence stability by a factor of 3.8. This research provides new theoretical support and practical tools for optimal scheduling of E-HIES under multiple uncertainties. Full article
(This article belongs to the Section Energy Systems)
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17 pages, 999 KB  
Article
A Unified Real Options Framework for Natural Gas Storage: Integrating Market Regimes and Cross-Market Spillovers
by Prosper Lamothe Fernández, Fernando Gallardo Olmedo and Hamidreza Abshenasan
Commodities 2026, 5(2), 11; https://doi.org/10.3390/commodities5020011 - 29 May 2026
Viewed by 247
Abstract
Natural gas markets exhibit violent, non-linear volatility regimes. The 2022 energy crisis introduced persistent supply shocks and cross-Atlantic spillover effects. Traditional valuation models assume single-regime environments; consequently, they systematically misprice storage assets during extreme stress. We propose a valuation framework tailored to these [...] Read more.
Natural gas markets exhibit violent, non-linear volatility regimes. The 2022 energy crisis introduced persistent supply shocks and cross-Atlantic spillover effects. Traditional valuation models assume single-regime environments; consequently, they systematically misprice storage assets during extreme stress. We propose a valuation framework tailored to these specific market volatilities. By integrating a hidden Markov model (HMM) and Diebold–Yilmaz (DY) spillover indices into a stochastic dynamic programming (SDP) engine, the framework isolates the persistence of stressed market conditions. The model captures structural arbitrage opportunities. We demonstrate a 197 percent net present value (NPV) premium over conventional benchmarks using synthetic data. The optimal policy expands inventory holding periods during high spillover intensity. The algorithm executes decisions with sub-millisecond latency. This approach provides a computationally viable tool for high-frequency risk management. Full article
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18 pages, 614 KB  
Article
Time-Varying Rare Disasters, Model Uncertainty, and the Equity Premium Puzzle
by Yuzhuo Ren and Weiqi Liu
Mathematics 2026, 14(11), 1791; https://doi.org/10.3390/math14111791 - 22 May 2026
Viewed by 168
Abstract
This study develops a production-based asset pricing model that incorporates time-varying disaster risk together with model uncertainty. Within an extended relative-entropy framework, agents’ distorted beliefs and ambiguity aversion are characterized, and the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation is derived under a stochastic robust-control setting. [...] Read more.
This study develops a production-based asset pricing model that incorporates time-varying disaster risk together with model uncertainty. Within an extended relative-entropy framework, agents’ distorted beliefs and ambiguity aversion are characterized, and the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation is derived under a stochastic robust-control setting. The framework implies that the equity premium can be decomposed into three components: diffusion and jump risk premiums associated with conventional risk aversion and an additional rare-event premium generated by ambiguity aversion. Numerical experiments show that ambiguity aversion reduces the equilibrium risk-free rate, whereas aversion to rare disasters significantly raises compensation for bearing risk, helping reconcile both the equity premium puzzle and the risk-free rate puzzle. In addition, equity return volatility increases with the probability of disaster events, but at a diminishing rate. Overall, the results underscore the importance of model uncertainty and time-varying disaster risk in the determination of asset prices and risk premia. Full article
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26 pages, 6226 KB  
Article
Three-Stage Stochastic Optimal Operation and Game-Theoretic Benefit Allocation Strategy for a PV-Storage Virtual Power Plant Under Multi-Market Synergy
by Xiang Li, Gaoquan Ma, Bangcan Wang, Na Cai, Junwei Bao, Zishi Wang, Xuan Yang, Qian Ai and Chenyang Zhao
Electronics 2026, 15(10), 2201; https://doi.org/10.3390/electronics15102201 - 20 May 2026
Viewed by 262
Abstract
To address the output volatility of distributed photovoltaics, the low utilization efficiency of energy storage resources, and the challenge of optimal revenue for PV-storage virtual power plants (VPPs) in multi-market environments, this paper proposes a three-stage stochastic optimal operation strategy for PV-storage VPPs [...] Read more.
To address the output volatility of distributed photovoltaics, the low utilization efficiency of energy storage resources, and the challenge of optimal revenue for PV-storage virtual power plants (VPPs) in multi-market environments, this paper proposes a three-stage stochastic optimal operation strategy for PV-storage VPPs under multi-market synergy and develops a benefit allocation model based on the Nash–Harsanyi bargaining game. A Monte Carlo simulation was adopted to capture the uncertainties of market electricity prices and PV power output, and the stochastic dual-dynamic-programming (SDDP) algorithm was employed to solve the three-stage optimization framework consisting of day-ahead bidding, real-time optimization, and real-time frequency regulation. Bargaining power was quantified from four dimensions—the marginal contribution rate, PV prediction accuracy, energy storage capacity, and utilization rate—to establish a fair and reasonable internal benefit allocation mechanism. Case studies verified that the proposed method improved the single-day market revenue by up to 20.79% compared with traditional operation modes, achieved a near-zero curtailment rate for distributed PV, and maintained frequency regulation performance scores above 0.4 at all times. The benefits of all investment entities in the alliance increased by 3.36–99.43%, significantly enhancing the multi-market profitability of PV-storage VPPs and the stability of alliance cooperation. Full article
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