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Keywords = capital assets pricing model

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25 pages, 12397 KB  
Article
Downside-Sensitive Portfolio Optimization and Risk Overlays for Real Estate Securities
by Dilmi C. W. Hettiachchi-Halpe-Kankanamalage, Abootaleb Shirvani, Nicholas Appiah, Svetlozar T. Rachev, W. Brent Lindquist and Frank J. Fabozzi
J. Risk Financial Manag. 2026, 19(6), 385; https://doi.org/10.3390/jrfm19060385 - 26 May 2026
Viewed by 223
Abstract
We employ an empirical framework for real estate securities that incorporates portfolio optimization, return distribution tail diagnostics, risk metrics, modeling of long-range dependence in return volatility, regression against benchmark indices, and option pricing, treating these as necessary layers of a risk-management structure that [...] Read more.
We employ an empirical framework for real estate securities that incorporates portfolio optimization, return distribution tail diagnostics, risk metrics, modeling of long-range dependence in return volatility, regression against benchmark indices, and option pricing, treating these as necessary layers of a risk-management structure that concentrates on downside risk. Optimization compared mean–variance against downside-sensitive conditional value at risk. Tail behavior was assessed via skewness, kurtosis, and extreme value theory; volatility persistence was examined using ARMA–FIGARCH models. Benchmark dependence was examined via the capital asset pricing model (CAPM), employing endogenous and exogenous market proxies. Insurance instruments via European options were priced using a doubly subordinated normal inverse Gaussian pricing model capable of modeling skewed, heavy-tailed return distributions. Significant findings for the optimized portfolios include return distributions with losses that are heavier-tailed than gains; a transition in time from moderate-to-high long-range dependence in conditional volatility; smaller values of CAPM “alpha” and “beta” for minimum-risk portfolios compared to tangent portfolios; and significant implied volatility values. Full article
(This article belongs to the Section Risk)
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32 pages, 2415 KB  
Article
Infrastructure Sharing as a Digital Platform Model for Sustainable Manufacturing: Lessons from Two Case Studies
by Mariusz Cholewa, Mateusz Molasy, Maria Rosienkiewicz and Joanna Helman
Sustainability 2026, 18(10), 5182; https://doi.org/10.3390/su18105182 - 21 May 2026
Viewed by 210
Abstract
Physical manufacturing and research infrastructures are essential for advanced innovation but often remain inaccessible to SMEs, start-ups, and research institutions that cannot justify ownership of capital-intensive assets. This study examines whether platform-mediated infrastructure sharing can function as a sustainable open-innovation mechanism in advanced [...] Read more.
Physical manufacturing and research infrastructures are essential for advanced innovation but often remain inaccessible to SMEs, start-ups, and research institutions that cannot justify ownership of capital-intensive assets. This study examines whether platform-mediated infrastructure sharing can function as a sustainable open-innovation mechanism in advanced manufacturing. Using the SCIP/SYNPRO platform developed in the SYNERGY and IDEATION projects, an exploratory case-study design combines descriptive analysis of a registry of 290 infrastructure items across 11 countries with qualitative analysis of 23 documented access requests, interaction records, and pilot reports. The results show that the Provider–Taker model facilitates observable access-enabling interactions, including infrastructure publication, request submission, provider–taker communication, negotiation, and selected documented use, although it does not measure population-wide access outcomes. Sharing potential is uneven: modular and emerging technologies, especially VR/AR infrastructures, attract higher request intensity than production-integrated assets. Users and providers favour negotiated access, flexible pricing, operator support, and contractual clarification rather than standardised rental models. Qualitative evidence shows that value is created through access to otherwise unavailable equipment, postponed investment, experimentation, technology familiarisation, student training, capability development, and new inter-organisational research links. The findings indicate that infrastructure sharing can support more resource-efficient innovation but depends on discoverability, governance, trust, and support mechanisms to scale. Full article
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21 pages, 6619 KB  
Article
GPF-EVMoLE: An ETS-Driven Variable Selection and Mixture-of-Experts Framework for Multi-Step Garlic Price Forecasting
by Xinran Yu, Ke Zhu, Honghua Jiang and Ruofei Chen
Sustainability 2026, 18(9), 4404; https://doi.org/10.3390/su18094404 - 30 Apr 2026
Viewed by 629
Abstract
Predicting garlic prices is difficult because the crop behaves as both an agricultural commodity and a speculative asset. Unlike staple grains, which follow more predictable seasonal supply cycles, garlic can be stored for over a year, its production is geographically concentrated, and its [...] Read more.
Predicting garlic prices is difficult because the crop behaves as both an agricultural commodity and a speculative asset. Unlike staple grains, which follow more predictable seasonal supply cycles, garlic can be stored for over a year, its production is geographically concentrated, and its demand remains inelastic. This industry structure makes it susceptible to speculative hoarding, where even minor harvest deficits may trigger sharp price spikes. A typical example is the “Suan Ni Hen” (crazy garlic) phenomenon in the Chinese market: during the 2009–2010 and 2016 periods, speculative capital repeatedly exploited expectations of harvest reduction to engage in large-scale hoarding. According to data released by China’s National Development and Reform Commission (NDRC) at the end of October 2016, national wholesale garlic prices surged by 90% year-on-year, with purchase prices in some major producing areas doubling or multiplying within a short period. Such short-term price bubbles, together with severe volatility and abrupt regime shifts, can make standard forecasting models unreliable in this uncertain environment. Existing methods, ranging from traditional seasonal algorithms to deep learning networks, often overlook the need to decouple the local trend-weekly-seasonal baseline from the dynamic effects of multi-source external signals. This paper proposes GPF-EVMoLE, a compositional multi-step forecasting framework built on an explicit division of labor. The framework first extracts an interpretable local trend and weekly-seasonal baseline through an ETS decomposition module. Two specialized components then process the residual signal: a temporal fusion Transformer-style variable selection network (VSN) uses multi-source external features to identify informative macroeconomic and environmental signals at each forecasting step, while a Mixture of Linear Experts (MoLE) models phase-wise regime shifts within the residual series. Together, these modules adaptively integrate heterogeneous information. This study evaluates the framework on a custom daily evaluation dataset containing 17,685 records across six major producing regions in three provinces. At 7-day and 14-day forecasting horizons, GPF-EVMoLE consistently outperforms eight representative statistical, machine learning, and deep learning baselines across MAE, RMSE, and MAPE metrics. Ablation studies verify the necessity of each component, showing that structural separation of the forecasting tasks helps overcome the limitations of monolithic models and provides an accurate and interpretable solution for complex agricultural markets. Full article
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17 pages, 592 KB  
Article
Modelling Extreme Losses in JSE Life Insurance Price Index Growth Rates Using the Generalised Extreme Value Distribution (GEVD) and the Generalised Pareto Distribution (GPD)
by Delson Chikobvu, Tendai Makoni and Frans Frederik Koning
Data 2026, 11(4), 86; https://doi.org/10.3390/data11040086 - 16 Apr 2026
Viewed by 441
Abstract
The life insurance sector plays a critical role in financial system stability but is inherently exposed to extreme market fluctuations due to long-term liabilities and asset–liability mismatches. This study investigates extreme losses in the growth rates of the JSE Life Insurance Price Index [...] Read more.
The life insurance sector plays a critical role in financial system stability but is inherently exposed to extreme market fluctuations due to long-term liabilities and asset–liability mismatches. This study investigates extreme losses in the growth rates of the JSE Life Insurance Price Index (LIPI) using the Generalised Extreme Value Distribution (GEVD) and the Generalised Pareto Distribution (GPD) under the Extreme Value Theory (EVT) framework. Monthly data from January 2000 to October 2023 were transformed into a loss series, and extreme events were captured using quarterly block maxima and a POT threshold at the 95th percentile. Model parameters were estimated through Maximum Likelihood Estimation, and downside risk was assessed using return levels, Value-at-Risk (VaR), and Tail Value-at-Risk (tVaR). The GEVD model produced a negative shape parameter, consistent with a bounded Weibull-type tail, while the GPD indicated a heavy-tailed distribution. Return level estimates show escalating loss magnitudes and widening uncertainty over longer horizons, reflecting the challenges of projecting rare events. Kupiec backtesting confirms the adequacy and reliability of the GEVD-based VaR across all confidence levels, whereas the GPD underestimates risk at lower thresholds. These findings indicate significant tail risk within the South African life insurance equity segment and underscore the importance of EVT-based risk measures for capital planning and regulatory oversight. The study contributes to financial risk modelling in the life insurance sector and offers practical insights for strengthening solvency assessment and enterprise risk management frameworks. Full article
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24 pages, 622 KB  
Article
How Do IFRS S2 Climate Risks Affect IAS 36 Impairments? A Constructive Accounting Framework Calibrated to European Steel
by Khaled Muhammad Hosni Sobehy, Lassaad Ben Mahjoub and Sahbi Gabsi
J. Risk Financial Manag. 2026, 19(4), 272; https://doi.org/10.3390/jrfm19040272 - 8 Apr 2026
Viewed by 1263
Abstract
A major connectivity gap arises from the misalignment between the forward-looking climate disclosures required by IFRS S2 and the historically rooted asset valuations mandated by IAS 36. This misalignment can cause the overvaluation of carbon-intensive assets and disrupt capital allocation decisions. This research [...] Read more.
A major connectivity gap arises from the misalignment between the forward-looking climate disclosures required by IFRS S2 and the historically rooted asset valuations mandated by IAS 36. This misalignment can cause the overvaluation of carbon-intensive assets and disrupt capital allocation decisions. This research specifically examines transition risks, such as carbon pricing, regulatory shocks, and technological disruption, and quantifies the financial externality using a combination of deterministic impairment testing and stochastic climate scenarios. We create a constructive framework and develop a model of a Synthetic Representative Firm, calibrated to major integrated steel producers in Europe. To generate nonlinear Green Swan shocks for Value-in-Use, the process combines Monte Carlo simulation with the Merton Jump-Diffusion model. This comparison shows the difference between the steady Management View and the volatile Market View. Empirical results reveal a material Sustainability Discount, representing a substantial erosion in the recoverable amount under IFRS S2 transition risk scenarios compared to the IAS 36 Deterministic Baseline. Simulations show a strong probability of asset stranding due to restricted cost pass-through, indicating that older assets may face elevated impairment risks under disorderly transition scenarios. Traditional deterministic models may not fully capture aspects of Double Materiality, potentially leaving balance sheets less responsive to transition risks. Integrating digitalization and the Circular Carbon Economy (CCE) framework presents a strategic method for averting value destruction. Therefore, this research supports the integration of stochastic transition risk modeling into impairment testing to achieve faithful financial representation. Full article
(This article belongs to the Topic Sustainable and Green Finance)
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35 pages, 585 KB  
Article
On Devising Carbon Offset Investments by Multiple-Objective Portfolio Selection and Exploring Multiple-Objective Capital Asset Pricing Models
by Yue Qi, Jianing Huang, Zhujun Qi and Yingying Li
Mathematics 2026, 14(6), 1080; https://doi.org/10.3390/math14061080 - 23 Mar 2026
Viewed by 486
Abstract
Humans face environmental deterioration. Scholars have identified carbon dioxide as one of the culprits, and they emphasize carbon offset. Researchers are investigating carbon offset investments. Some researchers have encouragingly deployed multivariate variational mode decomposition methods, but they have not fully optimized them. Some [...] Read more.
Humans face environmental deterioration. Scholars have identified carbon dioxide as one of the culprits, and they emphasize carbon offset. Researchers are investigating carbon offset investments. Some researchers have encouragingly deployed multivariate variational mode decomposition methods, but they have not fully optimized them. Some researchers have opportunely assessed capital asset pricing models, but they have not fully justified them. We devise multiple-objective portfolio selection models, fully optimize them, and dominate carbon offset indexes. We extend the classical methodology of advancing from portfolio selection to capital asset pricing models into the methodology of advancing from multiple-objective portfolio selection to multiple-objective capital asset pricing models. Specifically, we explore multiple-objective capital asset pricing models by numerically verifying many tangent lines (instead of the traditionally singular tangent line) and suggesting a tangent plane (instead of tangent lines). For multiple-objective zero-covariance capital asset pricing models, we numerically compute a set of zero-covariance portfolios (instead of the traditionally singular zero-covariance portfolio) and suggest picking an advantageous zero-covariance portfolio. We consider the second-level indicators of carbon offset and generalize three-objective portfolio selection to k-objective portfolio selection. As for contributions, first, this paper’s methodology is to logically advance from multiple-objective portfolio selection to multiple-objective capital asset pricing models, whereas the literature typically covers multiple-objective portfolio selection alone and barely covers multiple-objective capital asset pricing models. Second, this paper numerically demonstrates some difficulties and proposes hypothetical solutions in the process of obtaining multiple-objective capital asset pricing models. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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12 pages, 368 KB  
Article
On the Integro-Differential Equation Arising in the Ruin Problem for Non-Life Insurance Models with Investment
by Viktor Antipov and Yuri Kabanov
Mathematics 2026, 14(6), 1035; https://doi.org/10.3390/math14061035 - 19 Mar 2026
Viewed by 387
Abstract
In the classical non-life insurance models, the capital reserve of an insurance company increases at a constant rate and decreases by downward jumps. We consider a generalization of this model by supposing that a fixed portion of the capital reserve is continuously invested [...] Read more.
In the classical non-life insurance models, the capital reserve of an insurance company increases at a constant rate and decreases by downward jumps. We consider a generalization of this model by supposing that a fixed portion of the capital reserve is continuously invested in a risky asset whose price follows a geometric Brownian motion, while the complementary part is placed in a bank account with a constant rate of return. The quantity of interest is the ruin probability on the infinite time horizon as a function of the initial capital. In the present note, we assume only the continuity of the distribution of claims together with a standard moment restriction called “light tails.” Our main contribution is that we reveal, under such “minimalistic” hypotheses, that the ruin probability is smooth and satisfies a second-order integro-differential equation in the classical sense. We obtain the exact asymptotics for large values of the initial capital with “computable” constants and present results of numerical experiments. In contrast with other methods used in the theory, we rely upon only standard mathematics, allowing implementation in lecture courses for master’s students. Full article
(This article belongs to the Section E5: Financial Mathematics)
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23 pages, 2631 KB  
Article
A Novel Portfolio Selection Method via Deep Reinforcement Learning
by Ni Gao, Yan Liu, Yiyue He, Juan Zhang and Lefang Zhang
Systems 2026, 14(3), 292; https://doi.org/10.3390/systems14030292 - 9 Mar 2026
Viewed by 607
Abstract
Portfolio selection is a fundamental task in quantitative finance that aims to allocate capital across assets to balance risk and return. While deep learning has shown great promise in this field, extracting reliable feature representations from non-stationary and noisy financial data remains a [...] Read more.
Portfolio selection is a fundamental task in quantitative finance that aims to allocate capital across assets to balance risk and return. While deep learning has shown great promise in this field, extracting reliable feature representations from non-stationary and noisy financial data remains a significant challenge. The existing models often fail to simultaneously capture the temporal dynamics of price series and complex inter-asset correlations, which limits their trading performance. To address these issues, we propose Denoising-Sequence-Correlation Reinforcement Learning (DSCRL), a novel portfolio selection framework based on deep reinforcement learning. DSCRL employs a dual-stream feature extraction network, where one stream aims to learn temporal market dynamics and the other aims to capture asset correlations, enabling more informative representations. A denoising module is further integrated to mitigate the impact of noise, ensuring stability and robustness in the learning process. Furthermore, a deterministic policy gradient (DPG)-based decision network is designed to directly optimize continuous portfolio weights and normalize them to satisfy budget constraints while preserving the importance. Extensive experiments conducted on multiple benchmark datasets demonstrate that DSCRL consistently outperforms both traditional financial heuristics and advanced deep reinforcement approaches. The results highlight its superior ability to achieve higher cumulative returns with lower volatility. Overall, DSCRL provides an effective and robust solution that strikes a better trade-off between pursuing profits and managing risks in dynamic financial markets. Full article
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18 pages, 289 KB  
Article
Reassessing Residential REITs: Performance and Resilience After COVID-19
by Donna Seapoe, Anne Keenaghan and Davinder Malhotra
J. Risk Financial Manag. 2026, 19(3), 165; https://doi.org/10.3390/jrfm19030165 - 26 Feb 2026
Viewed by 2098
Abstract
This study analyzes the monthly returns of residential real estate investment trusts (REITs) from 2010 through 2025, assessing how these investments performed both during and following the COVID-19 pandemic. Using Sharpe, Sortino, and Omega ratios and multi-factor asset pricing models, the study finds [...] Read more.
This study analyzes the monthly returns of residential real estate investment trusts (REITs) from 2010 through 2025, assessing how these investments performed both during and following the COVID-19 pandemic. Using Sharpe, Sortino, and Omega ratios and multi-factor asset pricing models, the study finds that residential REITs delivered stable risk-adjusted returns and improved downside protection relative to broad indices. Value-at-risk metrics confirmed their defensive nature, and portfolio optimization demonstrated diversification and volatility reduction when including residential REITs. Overall, residential REITs were shown to preserve capital and improve portfolio efficiency during market disruptions. Full article
(This article belongs to the Special Issue Real Estate Finance and Risk Management)
37 pages, 688 KB  
Article
Disclosing Information About the Asset Value Range in Market
by Jianhao Su and Yanliang Zhang
Mathematics 2026, 14(3), 428; https://doi.org/10.3390/math14030428 - 26 Jan 2026
Viewed by 570
Abstract
The information released to investors in financial markets takes various forms. We understand range information as information about the upper and lower bounds that the payoff of a risky asset may reach in the future. This study develops rational expectation models to explore [...] Read more.
The information released to investors in financial markets takes various forms. We understand range information as information about the upper and lower bounds that the payoff of a risky asset may reach in the future. This study develops rational expectation models to explore the market impacts of disclosing such information. Our model shows that its disclosure can decrease market price sensitivity to private signal and increase market liquidity. Furthermore, the market impact of its disclosure depends on the position and precision of the range disclosed. When the linear combination of private signal and noise trading volume is distant from the disclosed range, the reaction of price to a variation in private signal will almost vanish, whereas movement in the disclosed range can efficiently impact price. Under certain conditions, such as a high proportion of informed traders or a small size of noise trading in the market, disclosing range information is more likely to reduce asset price and raise capital cost. Full article
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17 pages, 1573 KB  
Article
From Risk to Returns: An Analysis of Asset Quality, Financial Ratios, and Market Valuation in Indian Banks
by Shireen Rosario and Sudha Mavuri
Risks 2026, 14(1), 16; https://doi.org/10.3390/risks14010016 - 13 Jan 2026
Viewed by 2099
Abstract
This study investigates the interplay between asset quality, financial ratios, and market valuation in Indian commercial banks over a twelve-year period (2014–2025). Using a hybrid approach combining Structural Equation Modeling, correlation analysis, and trend evaluation, the research examines whether Non-Performing Assets (NPAs) influence [...] Read more.
This study investigates the interplay between asset quality, financial ratios, and market valuation in Indian commercial banks over a twelve-year period (2014–2025). Using a hybrid approach combining Structural Equation Modeling, correlation analysis, and trend evaluation, the research examines whether Non-Performing Assets (NPAs) influence market capitalization directly or through Return on Equity (ROE) as an intermediary. The findings reveal that NPAs exert a significant negative impact on both ROE and market value, while Net Interest Margin (NIM) emerges as a strong positive determinant of valuation. Conversely, Capital Adequacy Ratio (CAR), though vital for regulatory compliance, shows no direct effect on market prices. Mediation analysis challenges conventional assumptions, indicating that profitability alone does not fully explain valuation dynamics. These insights underscore the need for integrated strategies addressing asset quality and operational efficiency, offering practical implications for policymakers, investors, and bank management in strengthening resilience and optimizing shareholder value. Full article
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30 pages, 561 KB  
Review
On Intensively Criticizing and Envisioning the Research on Multiple-Objective Portfolio Selection from the Perspective of Capital Asset Pricing Models
by Yue Qi, Jianing Huang and Yixuan Zhu
Mathematics 2026, 14(2), 216; https://doi.org/10.3390/math14020216 - 6 Jan 2026
Cited by 1 | Viewed by 405
Abstract
Nobel Laureate Markowitz originates portfolio selection as the birth of modern finance. Nobel Laureate Sharpe implements portfolio selection and originates capital asset pricing models. Nobel Laureate Fama also implements portfolio selection and originates zero-covariance capital asset pricing models. After these feats, researchers have [...] Read more.
Nobel Laureate Markowitz originates portfolio selection as the birth of modern finance. Nobel Laureate Sharpe implements portfolio selection and originates capital asset pricing models. Nobel Laureate Fama also implements portfolio selection and originates zero-covariance capital asset pricing models. After these feats, researchers have gradually realized additional objectives and have promisingly extended portfolio selection into multiple-objective portfolio selection. However, there hardly exists research to leap from multiple-objective portfolio selection to multiple-objective capital asset pricing models (as initiated by Markowitz and Sharpe in finance). Moreover, the extension is basically confined to the branches of mathematics, operations research, optimization, and computer sciences. Many researchers sufficiently review multiple-objective portfolio selection. However, the reviews are extensive. Instead, we intensively criticize and envision the research on multiple-objective portfolio selection from the perspective of capital asset pricing models by crystallizing the research limitations and heralding future directions. Specifically, we emphasize seven research limitations for multiple-objective portfolio optimization, multiple-objective capital asset pricing models, and multiple-objective zero-covariance capital asset pricing models. We also generalize from common three-objective portfolio selection to k-objective portfolio selection. Visually, we orchestrate figures to delineate the complexity. Theoretically, this paper heralds challenging but encouraging future directions. Pragmatically, this paper proposes a formulation for the multiple-objective nature of practical convolution in finance. Full article
(This article belongs to the Special Issue Applications of Mathematics Analysis in Financial Marketing)
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27 pages, 1371 KB  
Article
The Thermodynamic Cliff: Pricing the Climate Adaptation Gap in Digital Infrastructure
by Seyedarash Aghili and Mehmet Nurettin Uğural
Systems 2026, 14(1), 34; https://doi.org/10.3390/systems14010034 - 26 Dec 2025
Viewed by 1088
Abstract
Conventional climate-risk frameworks, ranging from ESG ratings to Integrated Assessment Models (IAMs), systematically underestimate physical risks by overlooking the non-linear physics that govern infrastructure failure. These top-down models perceive climate change as a manageable operational expense, thereby obscuring the substantial capital requirements necessary [...] Read more.
Conventional climate-risk frameworks, ranging from ESG ratings to Integrated Assessment Models (IAMs), systematically underestimate physical risks by overlooking the non-linear physics that govern infrastructure failure. These top-down models perceive climate change as a manageable operational expense, thereby obscuring the substantial capital requirements necessary to sustain system reliability as global temperatures escalate. This study proposes a physics-first framework to quantify the “Adaptation Gap”—a measurable, unaccounted-for capital liability representing the additional cost needed to upgrade assets to maintain fault tolerance. Within this specific geographic and asset context, it has been determined that restoring fault tolerance for new equipment necessitates a 19.7% (95% CI: 16.5–22.9%) increase in capital expenditure, which increases the Adaptation Gap to 28.7% for typical in-service assets, potentially increasing the true cost for aging assets to between 25% and 30%. Although the quantitative findings are specific to the case study, the methodological framework—assessed as superior to traditional risk metrics—is designed for global application in pricing the Adaptation Gap across all infrastructure sectors with thermal constraints. Our methodology provides a blueprint for establishing a new standard of climate-adjusted valuation, transforming abstract physical risks into a tangible, auditable capital liability. Full article
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26 pages, 5326 KB  
Article
Short-Term Stock Market Reactions to Software Security Defects: An Event Study
by Xuewei Wang, Xiaoxi Zhang and Chunsheng Li
Systems 2026, 14(1), 14; https://doi.org/10.3390/systems14010014 - 24 Dec 2025
Viewed by 1699
Abstract
As enterprises increasingly depend on software systems, security defects such as vulnerability disclosures, exploitations, and misconfigurations have become economically relevant risk events. However, their short-term impacts on capital markets remain insufficiently understood. This study examines how different types of software security defects affect [...] Read more.
As enterprises increasingly depend on software systems, security defects such as vulnerability disclosures, exploitations, and misconfigurations have become economically relevant risk events. However, their short-term impacts on capital markets remain insufficiently understood. This study examines how different types of software security defects affect short-horizon stock market behavior. Using a multi-model event-study framework that integrates the Constant Mean Return Model (CMRM), Autoregressive Integrated Moving Average (ARIMA), and the Capital Asset Pricing Model (CAPM), we estimate abnormal returns and trading-activity responses around security-related events. The results show that vulnerability disclosures are associated with negative abnormal returns and reduced trading activity, while exploitation events lead to larger price declines accompanied by significant increases in trading activity. Misconfiguration incidents exhibit weaker price effects but persistent turnover increases, suggesting that markets interpret them primarily as governance-related issues. Further analyses reveal that market reactions vary with technical severity, exposure scope, industry context, and firm role, and that cyber shocks propagate through both price adjustment and liquidity migration channels. Overall, the findings indicate that software security defects act as short-term information shocks in financial markets, with heterogeneous effects depending on event type. This study contributes to the literature on cybersecurity economics and provides insights for firms, investors, and policymakers in managing software-related risks. Full article
(This article belongs to the Section Systems Practice in Social Science)
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28 pages, 1641 KB  
Article
Bayesian Estimation of R-Vine Copula with Gaussian-Mixture GARCH Margins: An MCMC and Machine Learning Comparison
by Rewat Khanthaporn and Nuttanan Wichitaksorn
Mathematics 2025, 13(23), 3886; https://doi.org/10.3390/math13233886 - 4 Dec 2025
Viewed by 1260
Abstract
This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally [...] Read more.
This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally intensive procedures limiting their practical use, we address this challenge through parallel computing techniques. To demonstrate our approach, we employ thirteen bivariate copula families within an R-vine pair-copula construction, applied to a large number of marginal distributions. The margins are modeled as exponential-type GARCH processes with intertemporal capital asset pricing specifications, using a mixture of Gaussian and generalized Pareto distributions. Results from an empirical study involving 100 financial returns confirm the effectiveness of our approach. Full article
(This article belongs to the Special Issue Contemporary Bayesian Analysis: Methods and Applications)
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