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32 pages, 2936 KB  
Article
Competitive Ranges of Timber, Concrete, and Steel Beams Based on Cost Optimization and Sensitivity Analysis, Including CO2 Emission Costs
by Stojan Kravanja and Tomaž Žula
Buildings 2026, 16(14), 2867; https://doi.org/10.3390/buildings16142867 - 18 Jul 2026
Viewed by 157
Abstract
This paper examines the competitive ranges of timber, steel, and reinforced concrete beams, determined using multi-parameter cost optimization that includes global warming costs (CO2 emissions) associated with beam production. Simply supported beams subjected to self-weight and uniform imposed loads were optimized using [...] Read more.
This paper examines the competitive ranges of timber, steel, and reinforced concrete beams, determined using multi-parameter cost optimization that includes global warming costs (CO2 emissions) associated with beam production. Simply supported beams subjected to self-weight and uniform imposed loads were optimized using discrete mixed-integer non-linear programming (MINLP). The objective functions included material, energy, labor, and CO2 emission costs associated only with manufacturing. Concrete remains the most cost-effective material across nearly all configurations, with glulam and steel being 2.3 and 2.8 times more expensive, respectively. Sawn timber outperforms concrete (by 9.5%) only at short spans (7.5 m) and low loads (10 kN/m1). Environmentally, timber yields the lowest manufacturing footprint, while steel and concrete emit 3.0 and 1.8 times more CO2 than glulam. Currently, CO2 emission costs average just 3.8% of total costs. However, a sensitivity analysis shows that extreme carbon taxes break concrete’s monopoly, increasing its costs by up to 637.4% and making timber the cheapest option for low-to-medium loads. Concrete is resilient to material price shocks at larger scales but highly vulnerable to rising labor rates (up to a 66.3% increase). While current carbon pricing is too low to influence material selection, future substantial tax escalations will shift structural competitiveness toward timber. Full article
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15 pages, 545 KB  
Article
IMEX–Crank–Nicolson Methods for the Merton Jump-Diffusion PIDE: Stability, Convergence, and Fast Jump Evaluation
by Mehran Paziresh, Karim Ivaz and Mariyan Milev
Axioms 2026, 15(7), 522; https://doi.org/10.3390/axioms15070522 - 13 Jul 2026
Viewed by 206
Abstract
This paper presents an efficient numerical framework for solving the Merton jump–diffusion partial integro-differential equation (PIDE) arising in European option pricing. To address the nonlocal integral term generated by asset price jumps, we employ an IMEX Crank–Nicolson time-stepping scheme that preserves the tri-diagonal [...] Read more.
This paper presents an efficient numerical framework for solving the Merton jump–diffusion partial integro-differential equation (PIDE) arising in European option pricing. To address the nonlocal integral term generated by asset price jumps, we employ an IMEX Crank–Nicolson time-stepping scheme that preserves the tri-diagonal structure of the resulting linear system. A nonuniform spatial grid and fast Gaussian quadrature with spline interpolation are incorporated to enhance accuracy and computational efficiency. We establish the unconditional stability and convergence of the IMEX–Crank–Nicolson scheme through a detailed theoretical analysis. Numerical experiments confirm the theoretical results and illustrate the effectiveness of the proposed method for representative jump–diffusion parameters. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications, 3rd Edition)
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22 pages, 2034 KB  
Article
Fixed-Point Analysis of Supra-Contractions with Applications to Nonlinear Economic Systems
by G. Sudhaamsh Mohan Reddy, Lateef Ahmad Wani, Mudasir Younis and Saiful R. Mondal
Mathematics 2026, 14(12), 2221; https://doi.org/10.3390/math14122221 - 20 Jun 2026
Viewed by 308
Abstract
In this article, we construct a framework for analyzing the equilibrium and stability of networked multi-sector economic systems via fixed-point analysis. We represent directional intersectoral dependencies, nonlinear feedback effects, and heterogeneous adjustment dynamics in the model by the coupled and tripled fixed-point theory [...] Read more.
In this article, we construct a framework for analyzing the equilibrium and stability of networked multi-sector economic systems via fixed-point analysis. We represent directional intersectoral dependencies, nonlinear feedback effects, and heterogeneous adjustment dynamics in the model by the coupled and tripled fixed-point theory in the graphically extended suprametric spaces. The graphical structure encodes supply-chain and influence networks, whereas asymmetric and nonuniform interaction strengths are encoded in the suprametric setting. Furthermore, we prove the existence, uniqueness, and convergence of equilibrium solutions under new generalized contraction conditions. We apply the theoretical findings in nonlinear state systems in which prices in interdependent markets are adjusted using integral equations. The results of numerical simulations show consistent convergence, and the sensitivity parameter of the network structure significantly influences the determination of economic stability and speed of adjustment. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)
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29 pages, 1872 KB  
Article
Point-in-Time Backtesting of Momentum-Trend Equity Strategies: A Formal Bias Taxonomy, ATR Trailing Stop Analysis, and Investor-Experience Metrics
by Xavier Fonseca
Mathematics 2026, 14(12), 2182; https://doi.org/10.3390/math14122182 - 17 Jun 2026
Viewed by 699
Abstract
Systematic trend-following strategies applied to equity markets are widely studied, yet most reported performance statistics are non-reproducible in live trading. This paper makes three contributions. First, we introduce a formal taxonomy of look-ahead bias organised around point-in-time correctness: a strategy is point-in-time correct [...] Read more.
Systematic trend-following strategies applied to equity markets are widely studied, yet most reported performance statistics are non-reproducible in live trading. This paper makes three contributions. First, we introduce a formal taxonomy of look-ahead bias organised around point-in-time correctness: a strategy is point-in-time correct if, for every decision time t, its information set lies in the natural filtration Ft. Three bias classes—universe-membership contamination, price-data forward leakage, and stop-exit sequencing violations—are characterised as filtration breaches. Second, we formalise the average true range (ATR) trailing stop as a stochastic recurrence and codify its monotonic non-decreasing ratcheting property (Lemma 1), providing a structural per-trade loss bound. Third, we exhibit a closed-form construction (Theorem 1) of two return sequences with identical Sharpe ratios but arbitrarily divergent maximum consecutive negative-year runs, establishing investor-experience metrics as independent optimisation objectives. We complement these contributions with an 18-year empirical study (2008–2025) on the NASDAQ-100 with reconstructed point-in-time index constituency (Class I compliant) and measured residual Class II exposure, applying combinatorially symmetric cross-validation (CSCV) to a 14-configuration ATR-multiplier grid. The grid exhibits a stop-multiplier-insensitive, CAGR-flat region across k[3.5,7.0] (CAGR 10.28–10.39%, net of Dutch progressive tax) and a uniform maximum consecutive negative-year run of 1 across all 14 configurations. The correlation-matrix eigenvalue spectrum of the grid is dominated by a single mode (λ1=13.91 of 14), yielding an effective independent-test count of Meff=1.09. This near-degeneracy persists in a parallel grid with the regime classifier disabled, establishing the ATR multiplier as a structurally near-redundant parameter for this strategy class. The associated PBO value of =0.9351 co-occurs with this near-degeneracy under the CSCV maximum-selection rule. The plateau-level performance survives Bonferroni correction for both M=14 and Meff. The combined evidence supports a region-based interpretation of robust strategy parameters rather than single-point optimisation. Full article
(This article belongs to the Special Issue New Advances in Mathematical Economics and Financial Modelling)
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26 pages, 3202 KB  
Article
What Shapes Regulated Electricity Contract Prices in a Hydro-Thermal Power System? Evidence from Colombia Using Quantile Regression and Autoencoders
by Andrés Oviedo-Gómez, Jose Daniel Minotta Saenz and Orlando Joaqui-Barandica
Electricity 2026, 7(2), 51; https://doi.org/10.3390/electricity7020051 - 4 Jun 2026
Viewed by 537
Abstract
This study examines the determinants of regulated electricity contract prices in Colombia during the period 2009–2021, with a particular focus on the role of electricity-market fundamentals and macroeconomic conditions. Although regulated contracts are designed to reduce exposure to short-term volatility, limited evidence exists [...] Read more.
This study examines the determinants of regulated electricity contract prices in Colombia during the period 2009–2021, with a particular focus on the role of electricity-market fundamentals and macroeconomic conditions. Although regulated contracts are designed to reduce exposure to short-term volatility, limited evidence exists on how their price formation behaves across different segments of the distribution. To address this issue, the analysis combines quantile regression with autoencoder-based dimensionality reduction, allowing the incorporation of a large set of macroeconomic variables without overparameterizing the model. The results show that regulated contract prices are more consistently associated with electricity-system factors than with broad macroeconomic conditions. In particular, the spot price becomes significant only in the upper quantiles, where it appears to operate as an indicator of operational stress, while hydropower and thermal generation exhibit localized effects across the distribution. By contrast, most macroeconomic factors display weak, uneven, or non-significant effects, with only the exchange-rate-related component becoming clearly relevant at relatively high price levels. A robustness analysis based on principal component analysis broadly supports these patterns. Overall, the evidence suggests that the Colombian regulated market behaves as a relatively stable contractual system, in which price formation is shaped mainly by electricity-sector conditions, indexation rules, and long-term risk-management mechanisms, while macroeconomic influences appear more limited and non-uniform across quantiles. Full article
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24 pages, 4193 KB  
Article
Agentic AI for Price-Only 15 min SDAC Market Diagnostics in Central and Eastern Europe
by Șener Ali, Simona-Vasilica Oprea and Adela Bâra
Appl. Syst. Innov. 2026, 9(5), 93; https://doi.org/10.3390/asi9050093 - 29 Apr 2026
Viewed by 1703
Abstract
The shift to 15 min market time units (MTUs) in single-day-ahead coupling (SDAC) increases temporal granularity, but complicates the interpretation of intra-hour electricity price spikes and rapid ramps. This paper examines whether architectural decomposition improves the reliability of large language model (LLM)-based diagnostics [...] Read more.
The shift to 15 min market time units (MTUs) in single-day-ahead coupling (SDAC) increases temporal granularity, but complicates the interpretation of intra-hour electricity price spikes and rapid ramps. This paper examines whether architectural decomposition improves the reliability of large language model (LLM)-based diagnostics in price-only settings, rather than causal market analytics, under severe information constraints. We compare a proposed agentic workflow featuring structured context extraction, spike/ramp detection, hypothesis generation, consistency checks, and explicit uncertainty calibration against non-agentic baselines. The paper contributes: (i) a reproducible benchmark for 15 min diagnostic question answering in day-ahead markets, (ii) an agentic architecture tailored to structured time-series reasoning with explicit uncertainty handling, and (iii) empirical evidence that decomposition and verification improve evidence grounding and trustworthiness in market analytics. The evaluation includes 360 price-only cases sampled across autumn 2025, winter 2025–2026, and early spring 2026, balanced by bidding zone, temporal period, event type, and impact tier, comprising 180 spike and 180 ramp cases from six Central and Eastern European bidding zones (Bulgaria, Czechia, Hungary, Poland, Romania, and Slovakia). Using identical inputs, we assess automatic reliability metrics and human ratings. The agentic workflow improves reliability (∆ = +0.067, 95% CI [+0.049, +0.085]) and significantly increases calibrated price-only disclaimers (∆ = +0.500) relative to the monolithic LLM baseline. Human evaluation confirms higher overall quality (+0.74), helpfulness (+1.06), and correctness (+0.94), with a 65.5% pairwise win rate. Overall, the results support a narrower conclusion: structured decomposition and verification improve calibration and perceived explanation quality relative to a simple monolithic LLM baseline, but their advantages are not uniform across stronger non-agentic baselines and remain limited by the absence of exogenous market data. Full article
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29 pages, 4647 KB  
Article
Hierarchical Day-Ahead Scheduling of a Wind–PV Hydrogen Production System Under TOU Electricity Prices
by Jun Liu, Wei Li, Wenjie Han, Xiaojie Liu, Guangchun Wang, Jie Wang, Zhipeng Chen, Yuanhang Xiong, Shaokang Zu and Jing Ma
Electronics 2026, 15(8), 1697; https://doi.org/10.3390/electronics15081697 - 17 Apr 2026
Viewed by 320
Abstract
To address the coupled challenges of renewable power volatility, high operating cost, and electrolyzer degradation in grid-connected wind–PV hydrogen production systems, this paper proposes a hierarchical day-ahead scheduling strategy under time-of-use (TOU) electricity prices. The upper layer performs price-responsive economic dispatch to coordinate [...] Read more.
To address the coupled challenges of renewable power volatility, high operating cost, and electrolyzer degradation in grid-connected wind–PV hydrogen production systems, this paper proposes a hierarchical day-ahead scheduling strategy under time-of-use (TOU) electricity prices. The upper layer performs price-responsive economic dispatch to coordinate renewable utilization, battery operation, grid transactions, and aggregate hydrogen-production power with the objective of minimizing lifecycle operating cost. The lower layer introduces a health-aware non-uniform rotation mechanism to allocate the aggregate power command among electrolyzer units, thereby reducing fluctuation exposure and balancing lifetime consumption across the array. Practical constraints, including multi-state electrolyzer operation, unit-commitment logic, battery state-of-charge dynamics, hydrogen storage limits, and system power balance, are explicitly considered. A case study of a wind–PV hydrogen production project in Northern China shows that the proposed strategy shifts electricity purchases to valley-price periods and promotes electricity export during peak-price periods. Compared with the benchmark strategy, hydrogen production during low wind–PV generation periods increases from 342,000 to 381,000 Nm3, the share of fluctuating operating time decreases from 62.5% to 12.5%, and the average daily start–stop frequency declines from 8.0 to 4.8. Consequently, the degradation penalty is reduced by about 40%, and lifecycle operating cost decreases by 27.3%. Full article
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31 pages, 3527 KB  
Article
The Assessment of Property Value Under EU Regulation 575/2013: An Operational Model for Italian Residential Market
by Paolo Rosato, Giovanni Florian and Matteo Galante
Real Estate 2026, 3(2), 3; https://doi.org/10.3390/realestate3020003 - 26 Mar 2026
Viewed by 767
Abstract
The correct valuation of collateral supporting real estate loans has always been a key issue for the stability of the credit system. Substandard lending practices and the absence of uniform valuation approaches have historically contributed to the accumulation of non-performing loans. In recent [...] Read more.
The correct valuation of collateral supporting real estate loans has always been a key issue for the stability of the credit system. Substandard lending practices and the absence of uniform valuation approaches have historically contributed to the accumulation of non-performing loans. In recent years, several regulatory measures operating at both the European and national level have introduced principles, rules and procedures aimed at standardizing the valuation of properties pledged as collateral for credit exposures. These interventions seek to promote greater transparency, consistency, and prudence in property appraisals, thereby enhancing the soundness and resilience of the financial system. In January 2025, the updated Regulation (EU) 575/2013 came into force, incorporating the Basel III reform (also referred to as Basel 3+ or Basel IV). Among the innovations introduced, the concept of property value (PV) is particularly relevant, a prudential value that excludes expectations of price growth and considers the sustainability of the value over time in relation to the duration of the loan. PV is defined as a derived value with respect to market value (MV), determined by considering the main current and forward-looking risk factors that may arise during the life of the loan, including environmental, social and governance (ESG) risks, the intrinsic characteristics of the property and expectations regarding the economic cycle. This paper proposes a quantitative model for the determination of PV, applied to a practical case involving a residential property located in a medium-sized city in Italy’s Veneto region. The model adopts a deterministic and a probabilistic approach, the latter implemented through Monte Carlo simulation, which is indeed a generalization of the deterministic one. The model links the assessment of PV to the possible evolution of the property’s key parameters and the real estate cycle over the duration of the loan. It was tested under the assumption of a twenty-year mortgage originated in 2025 for the purchase of a residential property in Italy, considering two alternative locations: a suburban area and a city-centre area. The analysis conducted showed a substantially higher MV haircut for the suburban property compared with the central location. This difference reflects the fact that PV is less sensitive to real estate cycle fluctuations in more premium, central locations. Furthermore, the use of Monte Carlo simulation in the probabilistic approach enabled the calibration of the haircut according to a predefined confidence level, confirming the pattern observed in the deterministic framework. The combined evidence strengthens the empirical robustness of the model and highlights the importance of locational and cyclical dynamics in collateral valuation. Full article
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36 pages, 776 KB  
Article
Carbon Risk Without a Stable Premium: Nonlinear and State-Dependent Evidence from European ESG Leaders
by Eleonora Salzmann
Risks 2026, 14(2), 41; https://doi.org/10.3390/risks14020041 - 20 Feb 2026
Viewed by 1157
Abstract
Despite the economic relevance of climate-transition risk, firm-level carbon exposure often fails to appear as a robustly priced factor when ESG measures and sustainability shocks are conflated. This study examines whether carbon exposure is conditionally priced in European equity returns using a strongly [...] Read more.
Despite the economic relevance of climate-transition risk, firm-level carbon exposure often fails to appear as a robustly priced factor when ESG measures and sustainability shocks are conflated. This study examines whether carbon exposure is conditionally priced in European equity returns using a strongly balanced quarterly panel of 238 firms from the MSCI Europe ESG Leaders universe (2018–2024). Total greenhouse gas emissions act as a proxy for carbon exposure, mapped to within-year percentiles and standardized by sector-year. Regressions control for ESG scores and controversies and include firm and quarter fixed effects with firm-clustered, dependence-robust standard errors. The linear carbon coefficient is small and statistically indistinguishable from zero, indicating no stable return premium from within-firm changes in carbon exposure. Functional-form tests reject linearity: quadratic and quintile specifications reveal curvature and a non-monotonic pattern, with return differences concentrated in the middle of the carbon distribution. Conditioning on macro-financial stress, measured by the ECB Composite Indicator of Systemic Stress, yields limited evidence of a uniform carbon penalty. However, high-controversy states are associated with lower returns, while ESG scores show negative associations under dependence-robust inference. Overall, carbon-related pricing appears to be nonlinear and state-dependent, whereas controversy risk is the most robust sustainability predictor of returns. Full article
13 pages, 1816 KB  
Article
Information-Processing Entropy and Heterogeneous Sentiment Reaction Windows: Evidence from S&P 500 Stocks
by Chi-Yao Peng
Entropy 2025, 27(12), 1234; https://doi.org/10.3390/e27121234 - 5 Dec 2025
Viewed by 734
Abstract
This study examines the heterogeneous timing of market responses to financial news and its implications for informational uncertainty in price-adjustment dynamics. Empirically, stocks do not incorporate positive and negative sentiment at the same speed; instead, they exhibit asset-specific delays that stem from differences [...] Read more.
This study examines the heterogeneous timing of market responses to financial news and its implications for informational uncertainty in price-adjustment dynamics. Empirically, stocks do not incorporate positive and negative sentiment at the same speed; instead, they exhibit asset-specific delays that stem from differences in investor attention, cognitive processing, and microstructural constraints. These unequal reaction windows increase the entropy of the information-transmission process, as sentiment shocks diffuse across assets in a dispersed and temporally misaligned manner. To quantify this heterogeneity, we develop a framework that integrates FinBERT-based sentiment classification, Bollinger Bands signal identification, and a Genetic Algorithm (GA) to estimate stock-specific sentiment reaction windows. Using S&P 500 data from 2021 to 2024, with 2022 to 2024 reserved for out-of-sample validation, the results show that GA-derived windows capture actual price-adjustment lags more accurately and significantly improve trading performance compared with fixed-window and technical-only benchmarks. In particular, incorporating news headline sentiment into the Bollinger Bands framework increases the win rate by approximately 5% over the testing period and leads to a significant improvement in overall returns. These findings demonstrate that the assimilation of sentiment is a time-dependent and non-uniform process shaped by behavioral and structural factors, offering new evidence that informational entropy—arising from delayed and heterogeneous reactions—plays a meaningful role in market efficiency and return dynamics. Full article
(This article belongs to the Section Multidisciplinary Applications)
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30 pages, 7297 KB  
Article
Nanofluid Cooling Enhances PEM Fuel Cell Stack Performance via 3D Multiphysics Simulation
by Rashed Kaiser, Se-Min Jeong and Jong-Chun Park
Energies 2025, 18(21), 5824; https://doi.org/10.3390/en18215824 - 4 Nov 2025
Cited by 1 | Viewed by 1452
Abstract
The proton-exchange membrane fuel cell (PEMFC) generates a significant reaction and ohmic heat during operation, imposing stringent cooling requirements. This study employs a three-dimensional, non-isothermal, steady multiphase multiphysics model to investigate heat generation and transport in a three-cell PEMFC stack using deionized water, [...] Read more.
The proton-exchange membrane fuel cell (PEMFC) generates a significant reaction and ohmic heat during operation, imposing stringent cooling requirements. This study employs a three-dimensional, non-isothermal, steady multiphase multiphysics model to investigate heat generation and transport in a three-cell PEMFC stack using deionized water, CuO, and Al2O3 nanofluids (1 vol%) as coolants. The base (no-coolant) configuration was validated against a published polarization curve for a nine-cell stack. Introducing coolant channels increased the area-averaged current density from 2426 A m−2 (no coolant) to 2613 A m−2 (water), 2678 A m−2 (CuO), and 2702 A m−2 (Al2O3), representing up to an 11.4% performance improvement while reducing the peak cell temperature by approximately 7–8 °C. Among the examined coolants, Al2O3 nanofluid achieved the lowest maximum temperature and a favorable pressure drop, whereas water maintained the most uniform temperature field. A price-performance factor (PPF) was introduced to evaluate the techno-economic trade-off between cost and cooling benefit. This study highlights that, despite scale-related limitations between three-cell simulations and nine-cell experiments, nanofluid coolants offer a practical route toward thermally stable and high-performance PEMFC operation. Full article
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22 pages, 2356 KB  
Article
A Study on Metal Futures Price Prediction Based on Piecewise Cubic Bézier Filtering for TCN
by Qingliang Zhao, Hongding Li, Qiangqiang Zhang and Yiduo Wang
Appl. Sci. 2025, 15(17), 9792; https://doi.org/10.3390/app15179792 - 6 Sep 2025
Cited by 2 | Viewed by 1676
Abstract
This study develops an effective forecasting model for metal futures prices with enhanced capability in trend identification and abrupt change detection, aiming to improve decision-making in both financial and industrial contexts. A hybrid framework is proposed that integrates non-uniform piecewise cubic Bézier curves [...] Read more.
This study develops an effective forecasting model for metal futures prices with enhanced capability in trend identification and abrupt change detection, aiming to improve decision-making in both financial and industrial contexts. A hybrid framework is proposed that integrates non-uniform piecewise cubic Bézier curves with a temporal convolutional network (TCN). The Bézier–Hurst (BH) decomposition extracts multi-scale trend components, which are then processed by a TCN to capture long-range dependencies. Empirical results show that the model outperforms LSTM, standard TCN, Bézier–TCN, and WD-TCN, achieving higher accuracy in trend detection and abrupt change response. This integration of Bézier-based decomposition with TCN offers a novel and robust tool for forecasting, providing valuable support for risk control and strategic planning in commodity markets. Full article
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15 pages, 2297 KB  
Article
Meshfree RBF-FD Discretization with Three-Point Stencils for Nonlinear Pricing Options Having Transaction Costs
by Haifa Bin Jebreen, Yurilev Chalco-Cano and Hongzhou Wang
Mathematics 2025, 13(17), 2839; https://doi.org/10.3390/math13172839 - 3 Sep 2025
Cited by 1 | Viewed by 1165
Abstract
This paper presents a computational framework for resolving a nonlinear extension of the Black–Scholes partial differential equation that accounts for transaction costs through a volatility function dependent on the Gamma of the option price. A meshfree radial basis function-generated finite difference procedure is [...] Read more.
This paper presents a computational framework for resolving a nonlinear extension of the Black–Scholes partial differential equation that accounts for transaction costs through a volatility function dependent on the Gamma of the option price. A meshfree radial basis function-generated finite difference procedure is developed using a modified multiquadric kernel. Analytical weight formulas for first- and second-order differentiations are discussed on 3-node stencils for both uniform and non-uniform point distributions. The proposed method offers an efficient scheme suitable for accurately pricing European scenarios when nonlinear transaction cost effects. Full article
(This article belongs to the Special Issue Financial Mathematics, 3rd Edition)
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37 pages, 3228 KB  
Article
Queuing Pricing with Time-Varying and Step Tolls: A Mathematical Framework for User Classification and Behavioral Analysis
by Chen-Hsiu Laih
Mathematics 2025, 13(13), 2192; https://doi.org/10.3390/math13132192 - 4 Jul 2025
Cited by 1 | Viewed by 987
Abstract
This study investigates user behavior at a bottleneck under two queuing pricing schemes: the optimal time-varying toll and the optimal multi-step toll. A mathematical model is developed to classify users based on toll status and arrival timing, further distinguishing between normal compliance and [...] Read more.
This study investigates user behavior at a bottleneck under two queuing pricing schemes: the optimal time-varying toll and the optimal multi-step toll. A mathematical model is developed to classify users based on toll status and arrival timing, further distinguishing between normal compliance and deliberate avoidance behaviors. Under the optimal time-varying toll, queuing is fully eliminated, no avoidance behavior occurs, and the user distribution remains consistent with the non-toll equilibrium. In contrast, the optimal n-step toll induces regular avoidance intervals before each toll change, with each interval exhibiting a uniform duration. The analysis reveals a structured classification of users into 3n + 2 behavioral groups, with predictable proportions in each category. These findings illustrate how step tolling affects user decision-making and temporal arrival patterns, offering valuable insights for the design of congestion pricing and traffic demand management strategies. Overall, the study highlights the practical applicability of queuing theory to transportation systems and contributes to the optimization of dynamic tolling mechanisms. Full article
(This article belongs to the Special Issue Recent Research in Queuing Theory and Stochastic Models, 2nd Edition)
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10 pages, 1294 KB  
Proceeding Paper
Resource Allocation in an Underwater Communication Network: The Stackelberg Game Power Control Method Based on a Non-Uniform Pricing Mechanism
by Xiangjie Luo and Hui Wang
Eng. Proc. 2025, 91(1), 10; https://doi.org/10.3390/engproc2025091010 - 17 Apr 2025
Viewed by 809
Abstract
In the following study, power allocation in underwater cooperative communication systems was investigated using game theory. To balance the energy consumption of nodes, extend their lifespan, and improve communication quality, a Stackelberg power control algorithm based on a non-uniform pricing mechanism was proposed. [...] Read more.
In the following study, power allocation in underwater cooperative communication systems was investigated using game theory. To balance the energy consumption of nodes, extend their lifespan, and improve communication quality, a Stackelberg power control algorithm based on a non-uniform pricing mechanism was proposed. The interaction model between the transmitting and relay nodes was constructed as a two-layer Stackelberg game, which consisted of leaders and followers. The transmitting node acts as the leader, with its objective function comprising its transmission cost and the purchasing transmission power cost of the relay nodes. The relay nodes act as followers, with their objective function comprising revenue from selling power and their transmission cost. In addition, the remaining energy is incorporated into the objective function to balance the energy consumption of the nodes. Our simulation results indicate that, compared with algorithms that do not consider remaining energy, this algorithm improves the communication quality of the cooperative system and extends the network’s lifetime. Full article
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