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Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 23668

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Dr. Pavol Durana

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Faculty of Operation and Economics of Transport and Communications, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovakia
Interests: corporate finance; financial management; economic statistics; qualitative and quantitative research
Special Issues, Collections and Topics in MDPI journals

Dr. Katarina Valaskova

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Faculty of Operation and Economics of Transport and Communications, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovakia
Interests: international financial markets; behavioural decision making; risk modelling; risk analysis; financial statistics
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Special Issue Information

Dear Colleagues,

Mathematical modeling is a fundamental academic matter to cover the endless drivers of change in economics. However, it also provides a preferred tool for economic development, sustainable business finance, and prosperous corporate life. These facts are supported by the conclusions of worldwide surveys and studies. The appropriate methods are run to select the best solutions or gain a competitive advantage for the enterprises as well as for the countries. Many entities use econometric modelling to know and forecast results in detail, not only vaguely without relationships and bonds. Comprehensive financial views may accelerate effective decisions for all the parties involved. Then, information asymmetry is reduced to get benefits and emphasize their impact. The executives can ensure key sources that are needed for crucial economic issues and innovation. The managers increase the probability of achieving financial goals, especially the expected earnings or avoiding the bankruptcy of the enterprises. Thus, this Special Issue focuses on the use of advanced methods of mathematical modeling in the topics presented and reflects recent methods used to face the challenges of business model transformation and optimization of corporate finance. Concerns also include how to adapt to new industries, products, ideas, and other parts of the global market and still be profitable.

We encourage researchers to submit original manuscripts that address the methods of the theory and application of mathematical modeling in economics, econometrics, and financial management. Each contribution must include a unique, never-before-published research strategy and approach.

Dr. Pavol Durana
Dr. Katarina Valaskova
Guest Editors

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Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

modeling in economics and financial management
financial econometrics
time series analysis and forecasting
modeling in corporate finance
prediction of bankruptcy and failure
earnings management

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Published Papers (9 papers)

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Research

16 pages, 938 KiB

Open AccessArticle

Optimal Tax Trajectory of a Commercial Organisation: Economic and Mathematical Approach

by Kristina Alekseyevna Zakharova, Danil Anatolyevich Muravyev, Vadim Vitalievich Ponkratov and Ekaterina Vladimirovna Degtyaryova

Mathematics 2024, 12(22), 3611; https://doi.org/10.3390/math12223611 - 19 Nov 2024

Viewed by 272

Abstract

The aim of this study is to form a new concept of tax burden calculation—optimal tax trajectory, which meets the needs of economic entities in view of the optimisation of tax payments and state authorities in terms of budget replenishment and subsequent efficient spending of state resources. The presented concept is developed on the basis of mathematical modelling of related economic processes. The model is based on the differential equation. An attempt is made to analyse the impact of building an optimal tax trajectory on the efficiency of the organisation’s activity. It shows that it is possible to increase the tax burden on economic entities in order to replenish the revenue part of the budget, which does not affect their financial situation. The proposed approach expands the instrumental apparatus for calculating tax payments from the position of taxpayers and fiscal authorities. The construction of the optimal tax trajectory facilitates the adoption of point decisions concerning the increase or decrease of the tax burden of an economic entity in mutual account with the factors of the macroeconomic conjuncture. This approach allows for managing the revenue part of the budget and redistributing it later to solve social problems or overcome business downturns. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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24 pages, 1196 KiB

Open AccessArticle

The Mathematical Simulation of South Korea’s Financial and Economic Impacts from Real Estate Bubbles: Lessons from the China Evergrande Collapse

by Dongxue Wang and Yugang He

Mathematics 2024, 12(19), 3058; https://doi.org/10.3390/math12193058 - 29 Sep 2024

Viewed by 1401

Abstract

This study investigates the macroeconomic and financial repercussions of a real estate bubble burst in South Korea through the application of Bayesian estimation and impulse response function analysis. By utilizing this approach tailored to the specific economic conditions of South Korea, the research effectively captures the complex ripple effects across a range of financial and macroeconomic variables. The results demonstrate that a real estate bubble burst markedly increases financial market risks, leading to heightened liquidity demands within the banking sector and necessitating adjustments in both deposit rates and bond yields. The study also emphasizes the differentiated impacts on patient and impatient households, where wealth losses drive significant shifts in consumption and labor supply behaviors, further constrained by prevailing labor market conditions. Additionally, the broader economic implications are examined, revealing the adverse effects on corporate output and investment, as well as the dynamics of international capital flows that impact foreign exchange reserves and exchange rates. These findings highlight the urgent need for proactive monitoring and policy interventions to mitigate the detrimental effects of real estate bubbles, ensuring financial stability and fostering sustainable economic growth in South Korea. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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14 pages, 740 KiB

Open AccessArticle

Effectiveness of Principal-Component-Based Mixed-Frequency Error Correction Model in Predicting Gross Domestic Product

by Yunxu Wang, Chi-Wei Su, Yuchen Zhang, Oana-Ramona Lobonţ and Qin Meng

Mathematics 2023, 11(19), 4144; https://doi.org/10.3390/math11194144 - 30 Sep 2023

Cited by 2 | Viewed by 1159

Abstract

As an important indicator that can reflect a country’s macroeconomic situation and future trend, experts and scholars have long focused on analyses and predictions of gross domestic product (GDP). Combining principal component analysis (PCA), the mixed-frequency data sampling (MIDAS) model and the error correction model (ECM), this investigation constructs the principal-component-based ECM-MIDAS and co-integration MIDAS (CoMIDAS) models, respectively. After that, this investigation uses the monthly consumption, investment and trade data to build a mixed-frequency model to predict quarterly GDP. The empirical results can be summarized as follows: First, the predictive effectiveness of the mixed-frequency model is better than that of the same-frequency model. Second, the three variables have a strong correlation, and applying the principal component idea when modelling the same and mixed frequencies can lead to more favourable predictive effectiveness. Third, adding an error correction term to the principal-component-based mixed-frequency model has a significant coefficient and a higher predictive accuracy. Based on the above, it can be concluded that combining the MIDAS model with error correction and a principal component is effective; thus, this combination may be applied to support real-time and accurate macroeconomic prediction. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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23 pages, 6171 KiB

Open AccessArticle

Industry 4.0: Marvels in Profitability in the Transport Sector

by Martin Bugaj, Pavol Durana, Roman Blazek and Jakub Horak

Mathematics 2023, 11(17), 3647; https://doi.org/10.3390/math11173647 - 23 Aug 2023

Cited by 4 | Viewed by 1513

Abstract

Despite the COVID-19 pandemic, the current era offers the ultimate possibility for prosperous corporate life, especially in the transport sector. Industry 4.0 covers artificial intelligence, big data, or industrial IoT, and thus spatial cognition algorithms, traffic flow prediction, autonomous vehicles, and smart sustainable mobility are not far away. The mentioned tools have already been implemented by enterprises in emerging countries. This exploration focused on transportation within the V4 region from 2016–2021. This article aims to confirm the positive sequel of applying Industry 4.0 to chosen indicators of profitability. The positive, negative, or no shift in the development of 534 businesses was based on Pettitt’s test. The Pearson chi-square test disclosed the significant dependency between Industry 4.0 and shifts in profitability ratios. Then, more than 25% of enterprises involved in Industry 4.0 had positive shifts in ROA, ROC, ROS, and ROR. The research proved not only its balanced effect but also its augmented force through the z-test of proportion. This investigation may provide multiple proofs for connected sectors with transportation to adapt the tools of Industry 4.0 and deliver the call for the governments in the V4 region to make this tool more achievable. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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25 pages, 2532 KiB

Open AccessArticle

Digital Twin Simulation Tools, Spatial Cognition Algorithms, and Multi-Sensor Fusion Technology in Sustainable Urban Governance Networks

by Elvira Nica, Gheorghe H. Popescu, Milos Poliak, Tomas Kliestik and Oana-Matilda Sabie

Mathematics 2023, 11(9), 1981; https://doi.org/10.3390/math11091981 - 22 Apr 2023

Cited by 62 | Viewed by 5237

Abstract

Relevant research has investigated how predictive modeling algorithms, deep-learning-based sensing technologies, and big urban data configure immersive hyperconnected virtual spaces in digital twin cities: digital twin modeling tools, monitoring and sensing technologies, and Internet-of-Things-based decision support systems articulate big-data-driven urban geopolitics. This systematic review aims to inspect the recently published literature on digital twin simulation tools, spatial cognition algorithms, and multi-sensor fusion technology in sustainable urban governance networks. We integrate research developing on how blockchain-based digital twins, smart infrastructure sensors, and real-time Internet of Things data assist urban computing technologies. The research problems are whether: data-driven smart sustainable urbanism requires visual recognition tools, monitoring and sensing technologies, and simulation-based digital twins; deep-learning-based sensing technologies, spatial cognition algorithms, and environment perception mechanisms configure digital twin cities; and digital twin simulation modeling, deep-learning-based sensing technologies, and urban data fusion optimize Internet-of-Things-based smart city environments. Our analyses particularly prove that virtual navigation tools, geospatial mapping technologies, and Internet of Things connected sensors enable smart urban governance. Digital twin simulation, data visualization tools, and ambient sound recognition software configure sustainable urban governance networks. Virtual simulation algorithms, deep learning neural network architectures, and cyber-physical cognitive systems articulate networked smart cities. Throughout January and March 2023, a quantitative literature review was carried out across the ProQuest, Scopus, and Web of Science databases, with search terms comprising “sustainable urban governance networks” + “digital twin simulation tools”, “spatial cognition algorithms”, and “multi-sensor fusion technology”. A Preferred Reporting Items for Systematic Reviews and Meta-analysis (PRISMA) flow diagram was generated using a Shiny App. AXIS (Appraisal tool for Cross-Sectional Studies), Dedoose, MMAT (Mixed Methods Appraisal Tool), and the Systematic Review Data Repository (SRDR) were used to assess the quality of the identified scholarly sources. Dimensions and VOSviewer were employed for bibliometric mapping through spatial and data layout algorithms. The findings gathered from our analyses clarify that Internet-of-Things-based smart city environments integrate 3D virtual simulation technology, intelligent sensing devices, and digital twin modeling. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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15 pages, 1072 KiB

Open AccessArticle

An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance

by Tao Liu, Malik Zaka Ullah, Stanford Shateyi, Chao Liu and Yanxiong Yang

Mathematics 2023, 11(4), 833; https://doi.org/10.3390/math11040833 - 7 Feb 2023

Cited by 7 | Viewed by 1643

Abstract

The Heston–Hull–White three-dimensional time-dependent partial differential equation (PDE) is one of the important models in mathematical finance, at which not only the volatility is modeled based on a stochastic process but also the rate of interest is assumed to follow a stochastic dynamic. Hence, an efficient method is derived in this paper based on the methodology of the localized radial basis function generated finite difference (RBF-FD) scheme. The proposed solver uses the RBF-FD approximations on graded meshes along all three spatial variables and a high order time-stepping scheme. Stability is also studied in detail to show under what conditions the proposed method is stable. Computational simulations are given to support the theoretical discussions. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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30 pages, 434 KiB

Open AccessArticle

Research on Corporate Indebtedness Determinants: A Case Study of Visegrad Group Countries

by Dominika Gajdosikova, Katarina Valaskova, Tomas Kliestik and Maria Kovacova

Mathematics 2023, 11(2), 299; https://doi.org/10.3390/math11020299 - 6 Jan 2023

Cited by 5 | Viewed by 2513

Abstract

Debt financing is arguably the most important source of external financing for enterprises and has become popular in recent years. Corporate debt is related to the monitoring of corporate indebtedness, which is a necessary part of evaluating the overall financial performance of an enterprise and will occur if an enterprise does not have enough equity. However, rising indebtedness can be a difficult financial situation for enterprises in the form of default and an inability to meet their emerging liabilities. The main aim of this paper is to perform a debt analysis of enterprises operating in the Visegrad Group countries and subsequently examine whether firm size and legal form have a statistically significant impact on selected indebtedness indicators. Firstly, it was necessary to perform a debt analysis using 10 debt ratios. Subsequently, the nonparametric Kruskal–Wallis test was used to perform a more detailed analysis focused on examining statistically significant differences in individual indebtedness ratios based on firm size and legal form. Bonferroni corrections were applied to detect where stochastic dominance occurred. The Kruskal–Wallis test results reveal statistically significant differences in debt ratios in Visegrad Group countries, confirming the impact of firm size and legal form on calculated debt ratios. Recognizing the impact of several determinants on corporate debt is critical because these firm-specific features may be interpreted as proxies for default probability or the volatility of corporate assets, which may simplify the decision-making processes of creditors and stakeholders. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

21 pages, 4493 KiB

Open AccessEditor’s ChoiceArticle

A Combined Model Based on Recurrent Neural Networks and Graph Convolutional Networks for Financial Time Series Forecasting

by Ana Lazcano, Pedro Javier Herrera and Manuel Monge

Mathematics 2023, 11(1), 224; https://doi.org/10.3390/math11010224 - 2 Jan 2023

Cited by 53 | Viewed by 6494

Abstract

Accurate and real-time forecasting of the price of oil plays an important role in the world economy. Research interest in forecasting this type of time series has increased considerably in recent decades, since, due to the characteristics of the time series, it was a complicated task with inaccurate results. Concretely, deep learning models such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) have appeared in this field with promising results compared to traditional approaches. To improve the performance of existing networks in time series forecasting, in this work two types of neural networks are brought together, combining the characteristics of a Graph Convolutional Network (GCN) and a Bidirectional Long Short-Term Memory (BiLSTM) network. This is a novel evolution that improves existing results in the literature and provides new possibilities in the analysis of time series. The results confirm a better performance of the combined BiLSTM-GCN approach compared to the BiLSTM and GCN models separately, as well as to the traditional models, with a lower error in all the error metrics used: the Root Mean Squared Error (RMSE), the Mean Squared Error (MSE), the Mean Absolute Percentage Error (MAPE) and the R-squared (R²). These results represent a smaller difference between the result returned by the model and the real value and, therefore, a greater precision in the predictions of this model. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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13 pages, 2553 KiB

Open AccessArticle

Dynamic Model of Enterprise Revenue Management Based on the SFA Model

by Aliya Alimhanova, Andrey Vazhdaev, Artur Mitsel and Anatoly Sidorov

Mathematics 2023, 11(1), 211; https://doi.org/10.3390/math11010211 - 31 Dec 2022

Cited by 1 | Viewed by 1672

Abstract

The actual problem of enterprise revenue management that requires an effective solution is considered. Revenue is the main source of cash proceeds specifically from the main enterprise activities, as well as one of the main factors affecting enterprise functioning. As a result, the amount of revenue is extremely important for the company—it must be sufficient to ensure the repayment of all expenses of the company and the formation of the required profit amount. However, the amount of revenue itself is not the only important characteristic of revenue; the revenue stability over time and the revenue receipt regularity are no less important. The purpose of this work is to develop a dynamic model of enterprise revenue management, which differs from the model known in the literature by considering the parameter of enterprise performance efficiency. The parametric method of Stochastic Frontier Analysis (SFA) is used as a method to evaluate the efficiency of an enterprise. Financial indicators are used as input and output data. The model was tested on six small business sectors of a single-industry town for the period from 2007 to 2021. Data collection was carried out using the SPARK system, which allows selecting enterprises for research by the status of the enterprise (bankrupt/operating), by the size of the enterprise (large/medium/small/micro), etc. The above calculations based on the constructed modified model have demonstrated the possibility of using the enterprise’s revenue management with the desired rate of change and with the work efficiency parameter. Full article

(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Economics, Econometrics, and Financial Management)

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