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15 pages, 2832 KiB  
Article
Processing of Low-Grade Cu–Pb–Zn Sulfide Polymetallic Ore Stockpiles for Sustainable Raw Material Recovery by Froth Flotation
by Michal Marcin, Martin Sisol, Martina Laubertová, Dominika Marcin Behunová and Igor Ďuriška
Processes 2025, 13(7), 2158; https://doi.org/10.3390/pr13072158 - 7 Jul 2025
Viewed by 354
Abstract
This study demonstrated the successful recovery of zinc, lead, and copper collective concentrates from historical metal-bearing mine tailings (sulfide–polymetallic ore with a composition of 7.38% Zn, 1.45% Pb, and 0.49% Cu) using froth flotation techniques, which were originally developed during uranium ore mining. [...] Read more.
This study demonstrated the successful recovery of zinc, lead, and copper collective concentrates from historical metal-bearing mine tailings (sulfide–polymetallic ore with a composition of 7.38% Zn, 1.45% Pb, and 0.49% Cu) using froth flotation techniques, which were originally developed during uranium ore mining. Froth flotation techniques were used to justify suitability for recovering metals. The effects of a dosage of the foaming agent Polyethylene glycol (PEG 600) at 50 and 100 g t−1, collector types Aerophine 3418A (AERO), Danafloat 067 (DF), and potassium ethyl xanthate (KEX) at 50 and 80 g t−1, and a suspension density of 300 and 500 g L−1 on froth flotation collective concentrates were investigated. The final collective concentrate achieved recoveries exceeding 91% for lead (Pb), 88% for copper (Cu), and 87% for zinc (Zn). The obtained concentrates were analyzed using Atomic Absorption Spectroscopy (AAS) and X-ray Fluorescence Spectrometry (XRF), while selected samples were further examined via Scanning Electron Microscopy (SEM) with Energy Dispersive X-ray Spectroscopy (EDS). The resulting sulfide concentrates can subsequently be treated using suitable hydrometallurgical techniques. The application of these concentrates in metal production would help reduce the environmental burden of mining activities. Full article
(This article belongs to the Special Issue Non-ferrous Metal Metallurgy and Its Cleaner Production)
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29 pages, 28225 KiB  
Review
Toxic Legacy—Environmental Impacts of Historic Metal Mining and Metallurgy in the Harz Region (Germany) at Local, Regional and Supra-Regional Levels
by Louisa Friederike Steingräber, Friedhart Knolle, Horst Kierdorf, Catharina Ludolphy and Uwe Kierdorf
Environments 2025, 12(7), 215; https://doi.org/10.3390/environments12070215 - 26 Jun 2025
Viewed by 1324
Abstract
As a legacy of historical metal mining and the processing and smelting of metalliferous ores, metal pollution is a serious environmental problem in many areas around the globe. This review summarizes the history, technical development and environmental hazards of historic metal mining and [...] Read more.
As a legacy of historical metal mining and the processing and smelting of metalliferous ores, metal pollution is a serious environmental problem in many areas around the globe. This review summarizes the history, technical development and environmental hazards of historic metal mining and metallurgical activities in the Harz Region (Germany), one of the oldest and most productive mining landscapes in Central Europe. The release of large amounts of metal-containing waste into rivers during historic ore processing and the ongoing leaching of metals from slag heaps, tailings dumps and contaminated soils and sediments are the main sources of metal pollution in the Harz Mountains and its foreland. This pollution extends along river systems with tributaries from the Harz Mountains and can even be detected in mudflats of the North Sea. In addition to fluvial discharges, atmospheric pollution by smelter smoke has led to long-term damage to soils and vegetation in the Harz Region. Currently, the ecological hazards caused by the legacy pollution from historical metal mining and metallurgy in the Harz Region are only partially known, particularly regarding the effects of changes in river ecosystems as a consequence of climate change. This review discusses the complexity and dynamics of human–environment interactions in the Harz Mountains and its surroundings, with a focus on lead (Pb) pollution. The paper also identifies future research directions with respect to metal contamination. Full article
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22 pages, 3940 KiB  
Article
Insights into the Process of Fish Diversity Pattern Changes and the Current Status of Spatiotemporal Dynamics in the Three Gorges Reservoir Area Using eDNA
by Jiaxin Huang, Yufeng Zhang, Xiaohan Dong, Xinxin Zhou, Zhihao Liu, Qiliang Chen, Fan Chen and Yanjun Shen
Fishes 2025, 10(6), 295; https://doi.org/10.3390/fishes10060295 - 18 Jun 2025
Cited by 1 | Viewed by 515
Abstract
The ecological consequences of the construction and operation of the Three Gorges Reservoir, particularly its unique operation strategy of storing clear water and releasing turbid water, exerts a profound influence on the composition and dynamics of local fish communities. To date, detailed and [...] Read more.
The ecological consequences of the construction and operation of the Three Gorges Reservoir, particularly its unique operation strategy of storing clear water and releasing turbid water, exerts a profound influence on the composition and dynamics of local fish communities. To date, detailed and comprehensive research on seasonal changes in the fish community across the entire reservoir remains scarce. This study aims to fill this research gap by systematically investigating fish diversity through a comprehensive assessment of six main river reaches and eight major tributaries. The investigation employs environmental DNA (eDNA) technology across three critical life-cycle stages: breeding, feeding, and overwintering periods. A total of 124 fish species were recorded, comprising 10 orders, 20 families, and 80 genera. The comparative analyses of historical data suggest a significant decline in lotic and endemic fish populations, accompanied by a concurrent increase in lentic, eurytopic, and non-native fish species. Notably, the composition of fish communities exhibited similarities between breeding and overwintering periods. This study highlights the occurrence of significant seasonal fluctuations in the fish communities, showing a preference for reservoir tails and tributaries as optimal habitats. Water temperature has a predominant influence on structuring fish communities within aquatic ecosystems. This study investigates variations in the biodiversity of fish communities using historical data, with a focus on changes linked to reservoir operations and water impoundment activities. By integrating historical data, this research examines changes in fish diversity that are associated with water storage processes. It provides foundational data on the current composition and diversity of fish communities within the watershed, elucidating the spatiotemporal variations in fish diversity and the mechanisms by which environmental factors influence these communities. Furthermore, the current study serves as a valuable reference for understanding the changes in fish communities within other large reservoirs. Full article
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16 pages, 8067 KiB  
Article
Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns
by Hamed Farahani and Rostislav A. Serota
Economies 2025, 13(6), 176; https://doi.org/10.3390/economies13060176 - 17 Jun 2025
Viewed by 309
Abstract
We studied decades-long (1980 to 2024) historic distributions of accumulated S&P500 returns, from daily returns to those over several weeks. The time series of the returns emphasize major upheavals in the markets—Black Monday, Tech Bubble, Financial Crisis, and the COVID pandemic—which are reflected [...] Read more.
We studied decades-long (1980 to 2024) historic distributions of accumulated S&P500 returns, from daily returns to those over several weeks. The time series of the returns emphasize major upheavals in the markets—Black Monday, Tech Bubble, Financial Crisis, and the COVID pandemic—which are reflected in the tail ends of the distributions. De-trending the overall gain, we concentrated on comparing distributions of gains and losses. Specifically, we compared the tails of the distributions, which are believed to exhibit a power-law behavior and possibly contain outliers. To this end, we determined confidence intervals of the linear fits of the tails of the complementary cumulative distribution functions on a log–log scale and conducted a statistical U-test in order to detect outliers. We also studied probability density functions of the full distributions of the returns with an emphasis on their asymmetry. The key empirical observations are that the mean of de-trended distributions increases near-linearly with the number of days of accumulation while the overall skew is negative—consistent with the heavier tails of losses—and depends little on the number of days of accumulation. At the same time, the variance of the distributions exhibits near-perfect linear dependence on the number of days of accumulation; that is, it remains constant if scaled to the latter. Finally, we discuss the theoretical framework for understanding accumulated returns. Our main conclusion is that the current state of theory, which predicts symmetric or near-symmetric distributions of returns, cannot explain the aggregate of empirical results. Full article
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20 pages, 2183 KiB  
Review
Bulk-Driven CMOS Differential Stages for Ultra-Low-Voltage Ultra-Low-Power Operational Transconductance Amplifiers: A Comparative Analysis
by Muhammad Omer Shah, Andrea Ballo and Salvatore Pennisi
Electronics 2025, 14(10), 2085; https://doi.org/10.3390/electronics14102085 - 21 May 2025
Viewed by 552
Abstract
Energy-efficient integrated circuits require scaled-down supply voltages, posing challenges for analog design, particularly for operational transconductance amplifiers (OTAs) essential in high-accuracy CMOS feedback systems. Below 1 V, gate-driven OTAs are limited in common-mode input range and minimum supply voltage. This work investigates CMOS [...] Read more.
Energy-efficient integrated circuits require scaled-down supply voltages, posing challenges for analog design, particularly for operational transconductance amplifiers (OTAs) essential in high-accuracy CMOS feedback systems. Below 1 V, gate-driven OTAs are limited in common-mode input range and minimum supply voltage. This work investigates CMOS Bulk-Driven (BD) sub-threshold techniques as an efficient alternative for ultra-low voltage (ULV) and ultra-low power (ULP) designs. Although BD overcomes MOS threshold voltage limitations, historical challenges like lower transconductance, latch-up, and layout complexity hindered its use. Recent advancements in CMOS processes and the need for ULP solutions have revived industrial interest in BD. Through theoretical analysis and computer simulations, we explore BD topologies for ULP OTA input stages, classifying them as tailed/tail-less and class A/AB, evaluating their effectiveness for robust analog design, while offering valuable insights for circuit designers. Full article
(This article belongs to the Special Issue Advanced CMOS Technologies and Applications)
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24 pages, 4411 KiB  
Article
Characterization of Historical Tailings Dam Materials for Li-Sn Recovery and Potential Use in Silicate Products—A Case Study of the Bielatal Tailings Dam, Eastern Erzgebirge, Saxony, Germany
by Kofi Moro, Nils Hoth, Marco Roscher, Fabian Kaulfuss, Johanes Maria Vianney and Carsten Drebenstedt
Sustainability 2025, 17(10), 4469; https://doi.org/10.3390/su17104469 - 14 May 2025
Cited by 1 | Viewed by 634
Abstract
The characterization of historical tailings bodies is crucial for optimizing environmental management and resource recovery efforts. This study investigated the Bielatal tailings dam (Altenberg, Germany), examining its internal structure, material distribution influenced by historical flushing technology, and the spatial distribution of valuable elements. [...] Read more.
The characterization of historical tailings bodies is crucial for optimizing environmental management and resource recovery efforts. This study investigated the Bielatal tailings dam (Altenberg, Germany), examining its internal structure, material distribution influenced by historical flushing technology, and the spatial distribution of valuable elements. To evaluate the tailings resource potential, drill core sampling was conducted at multiple points at a depth of 7 m. Subsequent analyses included geochemical characterization using sodium peroxide fusion, lithium borate fusion, X-ray fluorescence (XRF), and a scanning electron microscope with energy dispersive X-ray spectroscopy (SEM-EDX). Particle size distribution analysis via a laser particle size analyzer and wet sieving was conducted alongside milieu parameter (pH, Eh, EC) analysis. A theoretical assessment of the tailings’ potential for geopolymer applications was conducted by comparing them with other tailings used in geopolymer research and relevant European standards. The results indicated average concentrations of lithium (Li) of 0.1 wt%, primarily hosted in Li-mica phases, and concentrations of tin (Sn) of 0.12 wt%, predominantly occurring in cassiterite. Particle size analysis revealed that the tailings material is generally fine-grained, comprising approximately 60% silt, 32% fine sand, and 8% clay. These textural characteristics influenced the spatial distribution of elements, with Li and Sn enriched in fine-grained fractions predominantly concentrated in the dam’s central and western sections, while coarser material accumulated near injection points. Historical advancements in mineral processing, particularly flotation, had significantly influenced Sn distribution, with deeper layers showing higher Sn enrichment, except for the final operational years, which also exhibited elevated Sn concentrations. Due to the limitations of X-ray fluorescence (XRF) in detecting Li, a strong correlation between rubidium (Rb) and Li was established, allowing Li quantification via Rb measurements across varying particle sizes, redox conditions, and geological settings. This demonstrated that Rb can serve as a reliable proxy for Li quantification in diverse contexts. Geochemical and mineralogical analyses revealed a composition dominated by quartz, mica, topaz, and alkali feldspars. The weakly acidic to neutral conditions (pH 5.9–7.7) and reducing redox potential (Eh, 570 to 45 mV) of the tailings material indicated a minimal risk of acid mine drainage. Preliminary investigations into using Altenberg tailings as geopolymer materials suggested that their silicon-rich composition could serve as a substitute for coal fly ash in construction; however, pre-treatment would be needed to enhance reactivity. This study underscores the dual potential of tailings for element recovery and sustainable construction, emphasizing the importance of understanding historical processing techniques for informed resource utilization. Full article
(This article belongs to the Special Issue Geological Engineering and Sustainable Environment)
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17 pages, 2914 KiB  
Article
Investigation of the Possibilities for the Recycling of Mixed Heterogeneous Lead Refinery Waste
by Jasmina Dedić, Jelena Đokić, Gordana Milentijević, Irma Dervišević and Maja Petrović
Processes 2025, 13(5), 1380; https://doi.org/10.3390/pr13051380 - 30 Apr 2025
Viewed by 361
Abstract
The historical industrial waste deposit Gater was used to dispose of different metallurgy wastes from lead and zinc production. The metallurgical waste deposit was situated in the open space, between the tailing waste deposit Žitkovac and river Ibar flow. Large amounts of lead-containing [...] Read more.
The historical industrial waste deposit Gater was used to dispose of different metallurgy wastes from lead and zinc production. The metallurgical waste deposit was situated in the open space, between the tailing waste deposit Žitkovac and river Ibar flow. Large amounts of lead-containing wastes are produced in the non-ferrous metallurgical industry, such as lead ash and lead slag generated in Pb smelting, lead anode slime, and lead sludge produced in the raw lead refining process. In addition to the lead concentration, numerous valuable components are found in the lead refinery waste from the group of Critical Raw Materials, such as antimony, arsenic, bismuth, copper, nickel, magnesium, scandium, as well as Rare-Earth Elements. Samples with eight characteristic points were taken to obtain relevant data indicating a possible recycling method. The chemical composition analysis was conducted using ICP; the scanning was completed using SEM-EDS. The mineralogical composition was determined by using XRD. The chemical analysis showed a wide range of valuable metal concentrations, from Ag (in the range from 14.2 to 214.6, with an average 86.25 mg/kg) to heavy metals such as Cu (in the range from 282.7 to 28,298, with an average 10,683.7 mg/kg or 1.0683% that corresponds to some active mines), Ni and Zn (in the range from 1.259 to 69,853.4, with an average 14,304.81 mg/kg), Sc (in the range from 2.4 to 75.3, with an average 33.61 mg/kg), Pb (in the range from 862.6 to 154,027.5, with an average 45,046 mg/kg), Sb (in the range from 51.7 to 18,514.7, with an average 2267.8 mg/kg), Ca (in the range from 167.5 to 63,963, with an average 19,880 mg/kg), Mg (in the range from 668.3 to 76,824.5, with an average 31,670 mg/kg), and As (in the range from 62.9 to 24,328.1, with an average 5829.53 mg/kg). The mineralogy analysis shows that all metals are in the form of oxides, but in the case of As and Fe, SEM-EDS shows some portion of elemental lead, pyrite, and silica-magnesium-calcium oxides as slag and tailing waste residues. The proposed recovery process should start with leaching, and further investigation should decide on the type of leaching procedure and agents, considering the waste’s heterogeneous nature and acidity and toxicity. Full article
(This article belongs to the Special Issue Municipal Solid Waste for Energy Production and Resource Recovery)
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20 pages, 1830 KiB  
Article
The t-Distribution in Financial Mathematics and Multivariate Testing Contexts
by Eugene Seneta and Thomas Fung
J. Risk Financial Manag. 2025, 18(5), 224; https://doi.org/10.3390/jrfm18050224 - 22 Apr 2025
Cited by 1 | Viewed by 450
Abstract
The Student’s t-distribution provides a thematic connection between the historical and technical elements of this paper. The historical section offers a brief account of the early contributions of Chris Heyde and his collaborations with Madan and Seneta in the development of financial [...] Read more.
The Student’s t-distribution provides a thematic connection between the historical and technical elements of this paper. The historical section offers a brief account of the early contributions of Chris Heyde and his collaborations with Madan and Seneta in the development of financial mathematics. The technical section focuses on hypothesis testing, motivated by the observation that, in a setting with pairwise exchangeable dependence for test statistics, the cutoff methods proposed by Sarkar and colleagues in 2016 can be viewed as a first iteration of the classical approach developed by Holm in 1979. These methods had already been refined earlier by Seneta and Chen in their work from 1997 and 2005, which laid the foundation for further improvements. Building on this, a new iteration of the Seneta-Chen method is presented, offering enhancements over the Sarkar approach. Numerical and graphical comparisons are provided, focusing on equal tails testing within the multivariate t-distribution framework. While the tabulated results clearly show improvements with the new procedure, the simulated family-wise error rates across varying correlations reveal only minor practical differences between the iterative methods. This suggests that, under suitable conditions, a single iteration suffices in practice. The paper concludes with personal reflections from the first author, sharing memories of Joe Gani and Chris Heyde, in keeping with the commemorative nature of this issue. Full article
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31 pages, 2469 KiB  
Article
A Dynamic Hidden Markov Model with Real-Time Updates for Multi-Risk Meteorological Forecasting in Offshore Wind Power
by Ruijia Yang, Jiansong Tang, Ryosuke Saga and Zhaoqi Ma
Sustainability 2025, 17(8), 3606; https://doi.org/10.3390/su17083606 - 16 Apr 2025
Cited by 1 | Viewed by 954
Abstract
Offshore wind farms play a pivotal role in the global transition to clean energy but remain susceptible to diverse meteorological hazards—ranging from highly variable wind speeds and temperature anomalies to severe oceanic disturbances—that can jeopardize both turbine safety and overall power output. Although [...] Read more.
Offshore wind farms play a pivotal role in the global transition to clean energy but remain susceptible to diverse meteorological hazards—ranging from highly variable wind speeds and temperature anomalies to severe oceanic disturbances—that can jeopardize both turbine safety and overall power output. Although Hidden Markov Models (HMMs) have a longstanding track record in operational forecasting, this study leverages and extends their capabilities by introducing a dynamic HMM framework tailored specifically for multi-risk offshore wind applications. Building upon historical datasets and expert assessments, the proposed model begins with initial transition and observation probabilities and then refines them adaptively through periodic or event-triggered recalibrations (e.g., Baum–Welch), thus capturing evolving weather patterns in near-real-time. Compared to static Markov chains, naive Bayes classifiers, and RNN (LSTM) baselines, our approach demonstrates notable accuracy gains, with improvements of up to 10% in severe weather conditions across three industrial-scale wind farms. Additionally, the model’s minutes-level computational overhead for parameter updates and state decoding proves feasible for real-time deployment, thereby supporting proactive scheduling and maintenance decisions. While this work focuses on the core dynamic HMM method, future expansions may incorporate hierarchical structures, Bayesian uncertainty quantification, and GAN-based synthetic data to further enhance robustness under high-dimensional measurements and rare, long-tail meteorological events. In sum, the multi-risk forecasting methodology presented here—though built on an established HMM concept—offers a practical, adaptive solution that significantly bolsters safety margins and operational reliability in offshore wind power systems. Full article
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23 pages, 10335 KiB  
Article
Multitemporal Spatial Analysis for Monitoring and Classification of Coal Mining and Reclamation Using Satellite Imagery
by Koni D. Prasetya and Fuan Tsai
Remote Sens. 2025, 17(6), 1090; https://doi.org/10.3390/rs17061090 - 20 Mar 2025
Viewed by 1520
Abstract
Observing coal mining and reclamation activities using remote sensing avoids the need for physical site visits, which is important for environmental and land management. This study utilizes deep learning techniques with a U-Net and ResNet architecture to analyze Sentinel imagery in order to [...] Read more.
Observing coal mining and reclamation activities using remote sensing avoids the need for physical site visits, which is important for environmental and land management. This study utilizes deep learning techniques with a U-Net and ResNet architecture to analyze Sentinel imagery in order to track changes in coal mining and reclamation over time in Tapin Regency, Kalimantan, Indonesia. After gathering Sentinel 1 and 2 satellite imagery of Kalimantan Island, manually label coal mining areas are used to train a deep learning model. These labelled areas included open cuts, tailings dams, waste rock dumps, and water ponds associated with coal mining. Applying the deep learning model to multitemporal Sentinel 1 and 2 imagery allowed us to track the annual changes in coal mining areas from 2016 to 2021, while identifying reclamation sites where former coal mines had been restored to non-coal-mining use. An accuracy assessment resulted in an overall accuracy of 97.4%, with a Kappa value of 0.91, through a confusion matrix analysis. The results indicate that the reclamation effort increased more than twice in 2020 compared with previous years’ reclamation. This phenomenon was mainly affected by the massive increase in coal mining areas by over 40% in 2019. The proposed method provides a practical solution for detecting and monitoring open-pit coal mines while leveraging freely available data for consistent long-term observation. The primary limitation of this approach lies in the use of medium-resolution satellite imagery, which may result in lower precision compared to direct field measurements; however, the ability to integrate historical data with consistent temporal coverage makes it a viable alternative for large-scale and long-term monitoring. Full article
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16 pages, 2274 KiB  
Article
A New Trick of Old Dogs: Can Kappa Opioid Receptor Antagonist Properties of Antidepressants Assist in Treating Treatment-Resistant Depression (TRD)?
by Shaul Schreiber, Lee Keidan and Chaim G. Pick
Pharmaceuticals 2025, 18(2), 208; https://doi.org/10.3390/ph18020208 - 3 Feb 2025
Viewed by 1848
Abstract
Background/Objectives: Approximately one in five individuals will experience major depressive disorder (MDD), and 30% exhibit resistance to standard antidepressant treatments, resulting in a diagnosis of treatment-resistant depression (TRD). Historically, opium was used effectively to treat depression; however, when other medications were introduced, its [...] Read more.
Background/Objectives: Approximately one in five individuals will experience major depressive disorder (MDD), and 30% exhibit resistance to standard antidepressant treatments, resulting in a diagnosis of treatment-resistant depression (TRD). Historically, opium was used effectively to treat depression; however, when other medications were introduced, its use was discontinued due to addiction and other hazards. Recently, kappa opioid receptor (KOR) antagonism has been proposed as a potential mechanism for treating TRD. The main research question is whether commonly used psychotropic medications possess KOR antagonist properties and whether this characteristic could contribute to their efficacy in TRD. Methods: We investigated the antinociceptive effects of many psychotropic medications and their interactions with the opioid system. Mice were tested with a hotplate or tail-flick after being injected with different doses of these agents. Results: The antidepressants mianserin and mirtazapine (separately) induced dose-dependent antinociception, each yielding a biphasic dose–response curve. Similarly, the antidepressant venlafaxine produced a potent effect and reboxetine produced a weak effect. The antipsychotics risperidone and amisulpride exhibited a dose-dependent antinociceptive effect. The sedative–hypnotic zolpidem induced a weak bi-phasic dose-dependent antinociceptive effect. All seven psychotropic medications elicited antinociception, which was reversed by the non-selective opiate antagonist naloxone and, separately, by the kappa-selective antagonist Nor-BNI. Conclusions: Clinical studies are mandatory to establish the potential efficacy of augmentation of the treatment with antidepressants with these drugs in persons with treatment-resistant depression and the optimal dosage of medications prescribed. We suggest a possible beneficial effect of antidepressants with kappa antagonistic properties. Full article
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12 pages, 597 KiB  
Article
Historical Simulation Systematically Underestimates the Expected Shortfall
by Pablo García-Risueño
J. Risk Financial Manag. 2025, 18(1), 34; https://doi.org/10.3390/jrfm18010034 - 15 Jan 2025
Cited by 2 | Viewed by 1529
Abstract
Expected Shortfall (ES) is a risk measure that is acquiring an increasingly relevant role in financial risk management. In contrast to Value-at-Risk (VaR), ES considers the severity of the potential losses and reflects the benefits of diversification. ES is often calculated using Historical [...] Read more.
Expected Shortfall (ES) is a risk measure that is acquiring an increasingly relevant role in financial risk management. In contrast to Value-at-Risk (VaR), ES considers the severity of the potential losses and reflects the benefits of diversification. ES is often calculated using Historical Simulation (HS), i.e., using observed data without further processing into the formula for its calculation. This has advantages like being parameter-free and has been favored by some regulators. However, the usage of HS for calculating ES presents a potentially serious drawback: It strongly depends on the size of the sample of historical data, being typically reasonable sizes similar to the number of trading days in one year. Moreover, this relationship leads to systematic underestimation: the lower the sample size, the lower the ES tends to be. In this letter, we present examples of this phenomenon for representative stocks and bonds, illustrating how the values of the ES and their averages are affected by the number of chosen data points. In addition, we present a method to mitigate the errors in the ES due to a low sample size, which is suitable for both liquid and illiquid financial products. Our analysis is expected to provide financial practitioners with useful insights about the errors made using Historical Simulation in the calculation of the Expected Shortfall. This, together with the method that we propose to reduce the errors due to finite sample size, is expected to help avoid miscalculations of the actual risk of portfolios. Full article
(This article belongs to the Section Risk)
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31 pages, 488 KiB  
Article
Natural Cubic Spline Approximation of Risk-Neutral Density
by Shuang Zhou, Liyuan Jiang, Keren Li, Fangfang Wang and Jie Yang
Int. J. Financial Stud. 2024, 12(4), 127; https://doi.org/10.3390/ijfs12040127 - 17 Dec 2024
Viewed by 1152
Abstract
The risk-neutral density is a fundamental concept in pricing financial derivatives, risk management, and assessing financial markets’ perceptions over significant political or economic events. In this paper, we propose a new nonparametric method for estimating the risk-neutral density using natural cubic splines (NCS). [...] Read more.
The risk-neutral density is a fundamental concept in pricing financial derivatives, risk management, and assessing financial markets’ perceptions over significant political or economic events. In this paper, we propose a new nonparametric method for estimating the risk-neutral density using natural cubic splines (NCS). The estimated density is twice continuously differentiable with linear tails at both ends. Our method targets the logarithm of the underlying asset price, releasing the restriction to the positive domain. We theoretically prove the consistency of our NCS method. We conduct a comprehensive empirical study comparing the proposed NCS method with a piecewise constant method, a uniform quartic B-spline method, and a cubic spline method from the literature using 20 years of S&P 500 index option data. The empirical results show that our NCS method is more robust than the piecewise constant method, which can only produce a discontinuous density, especially for options with maturities longer than six months. Moreover, our NCS method outperforms other historical continuous methods in terms of optimization feasibility and option price estimation. Full article
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29 pages, 2519 KiB  
Article
Fitting the Seven-Parameter Generalized Tempered Stable Distribution to Financial Data
by Aubain Nzokem and Daniel Maposa
J. Risk Financial Manag. 2024, 17(12), 531; https://doi.org/10.3390/jrfm17120531 - 22 Nov 2024
Cited by 1 | Viewed by 1083
Abstract
This paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes maximum-likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the [...] Read more.
This paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes maximum-likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), we provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavy-tailed data (Bitcoin and Ethereum returns) and two peaked data (S&P 500 and SPY ETF returns). For each historical data, the estimation results show that six-parameter estimations are statistically significant except for the local parameter, μ. The goodness of fit was assessed through Kolmogorov–Smirnov, Anderson–Darling, and Pearson’s chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the GTS distribution fits significantly with a very high p-value and outperforms the Kobol, Carr–Geman–Madan–Yor, and bilateral Gamma distributions. Full article
(This article belongs to the Special Issue Featured Papers in Mathematics and Finance)
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17 pages, 3831 KiB  
Article
Assessing the Recreational Resource Value of National Park Based on Visitor Perception—A Case of Three-River-Source National Park in China
by Xiao Luo, Zongcai Huang and Lingen Wang
Land 2024, 13(11), 1882; https://doi.org/10.3390/land13111882 - 11 Nov 2024
Cited by 3 | Viewed by 1172 | Correction
Abstract
National parks serve as critical practical sites for advancing the concept of “harmonious coexistence between humans and nature” and hold a strategic role in establishing global ecological security barriers. Scholars and decision-makers have expressed significant interest in rigorous assessments of the recreational resource [...] Read more.
National parks serve as critical practical sites for advancing the concept of “harmonious coexistence between humans and nature” and hold a strategic role in establishing global ecological security barriers. Scholars and decision-makers have expressed significant interest in rigorous assessments of the recreational resource value in national parks. This paper focuses on the Three-River-Source National Park, examining the characteristics and components of its recreational resource value through the lens of human–environment relationship theory. Analysis spans dimensions of geological and geomorphological value, ecological service value, historical and cultural value, and aesthetic landscape value. By extracting visitor comments rich in vocabulary related to their perceptions, this study compares variations in resource values and the “resource value–visitor perception” synergy within Three-River-Source National Park, employing text analysis, semantic network analysis, and coordination analysis methods. The findings reveal that (1) Visitor perceptions of recreational resource value display a clear hierarchy, with aesthetic landscape value (43.6%) ranking highest, followed by geological and geomorphological value (26.7%), historical and cultural value (19.3%), and ecological service value (10.4%), showing significant variation among categories; the vocabulary across these value types exhibits a pronounced long-tail distribution. (2) The recreational resource value in the park forms a distinct core centered on prominent attractions, accompanied by patterns of vocabulary aggregation and dispersion. (3) Visitors demonstrate strong synergy in their perception of geological and aesthetic value, weaker perception regarding historical and cultural value, and a relatively narrow understanding of ecological service value. This research enhances public comprehension of the recreational resource value of national parks and provides a scientific foundation for the conservation and sustainable use of recreational resources in national parks, advancing the realization of their recreational functions. Full article
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