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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: closed (31 July 2023) | Viewed by 30348

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Special Issue Editor

Prof. Dr. Vladimir A. Plotnikov

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Guest Editor

Department of General Economic Theory and History of Economic Thought, St. Petersburg State University of Economics, Sadovaya Str. 21, 191023 St. Petersburg, Russia
Interests: strategic planning; business; strategic management; governance; management; leadership; business development; entrepreneurship; innovation; human resource management

Special Issue Information

Dear Colleagues,

Mathematics is one of the universal sciences. Mathematical tools are successfully used to solve various problems in technical and natural sciences. However, for social and economic research, mathematical methods have not yet received the same widespread use. There is great potential in the use of mathematical methods in economics and finance.

For this, technical opportunities have appeared today (the development of information and communication technologies—Big Data, Neural Networks, Intelligent Systems, etc., and the emergence of the digital economy). This creates the preconditions for a more active introduction of mathematical achievements in the field of economics and finance.

The purpose of this Special Issue is a collection of articles on the development and implementation of advanced mathematical and instrumental methods in the field of economics and finance. These methods can be based on traditional modeling and forecasting tools, and on the new tools associated with the development of intelligent digital technologies.

Prof. Dr. Vladimir A. Plotnikov
Guest Editor

Manuscript Submission Information

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.

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Keywords

Economic mathematics
Financial Mathematics
Financial mathematics
Digital economy
Big data
Collaborative economy
Intelligent systems
Risk management
Economic modeling and forecasting
Managerial economics

Published Papers (13 papers)

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Research

15 pages, 342 KiB

Open AccessArticle

The Imbalanced Classification of Fraudulent Bank Transactions Using Machine Learning

by Alexey Ruchay, Elena Feldman, Dmitriy Cherbadzhi and Alexander Sokolov

Mathematics 2023, 11(13), 2862; https://doi.org/10.3390/math11132862 - 26 Jun 2023

Viewed by 2225

Abstract

This article studies the development of a reliable AI model to detect fraudulent bank transactions, including money laundering, and illegal activities with goods and services. The proposed machine learning model uses the CreditCardFraud dataset and utilizes multiple algorithms with different parameters. The results are evaluated using Accuracy, Precision, Recall, F1 score, and IBA. We have increased the reliability of the imbalanced classification of fraudulent credit card transactions in comparison to the best known results by using the Tomek links resampling algorithm of the imbalanced CreditCardFraud dataset. The reliability of the results, using the proposed model based on the TPOT and RandomForest algorithms, has been confirmed by using 10-fold cross-validation. It is shown that on the dataset the accuracy of the proposed model detecting fraudulent bank transactions reaches 99.99%. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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18 pages, 1208 KiB

Open AccessArticle

Fuzzy Model for Determining the Risk Premium to the Rental Rate When Renting Technological Equipment

by Yuriy Ekhlakov, Sergei Saprunov, Pavel Senchenko and Anatoly Sidorov

Mathematics 2023, 11(3), 541; https://doi.org/10.3390/math11030541 - 19 Jan 2023

Viewed by 1156

Abstract

The article is devoted to the method of determining the risk surcharge in rental rates for special technological equipment. The relevance and features of the task, as well as existing approaches to solve it in other subject areas, are described. The risk of landlords is highlighted as “the inability to fully ensure the receipt of a stable income recorded in the lease agreement”. The three most significant risk-forming factors are highlighted: the early return of equipment, the emergence of debt on payments from the tenant, and the breakdown of equipment due to the fault of the tenant. A fuzzy model for estimating the likelihood of the manifestation of risk-forming factors is proposed depending on the following challenges of the rental pillar: the size of the enterprise, financial stability, the age of the enterprise, the number of current trials, and the reputation of the enterprise. Describes: universal linguistics for input and output values characterizing risky components, logical output rules, and the assessment of the likelihood of risk in general. Based on the SciKit-Fuzzy library for the Python language, the model studies all available values of input variables, and tenants are presented separately on the boundary values of the enterprise parameters. A methodology for determining the rental rate, taking into account the risk surcharge, is proposed. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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13 pages, 602 KiB

Open AccessArticle

Validity of the Fama-French Three- and Five-Factor Models in Crisis Settings at the Example of Select Energy-Sector Companies during the COVID-19 Pandemic

by Konstantin B. Kostin, Philippe Runge and Leyla E. Mamedova

Mathematics 2023, 11(1), 49; https://doi.org/10.3390/math11010049 - 23 Dec 2022

Viewed by 1751

Abstract

This study empirically analyzes return data from select energy companies in developed and emerging markets using the Fama-French three- and five-factor asset-pricing models in crisis settings. It researches whether these models are suitable to produce meaningful return data in challenging economic circumstances. We use panel data covering 12 of the largest globally-operating energy companies from Russia, China, the US, the EU, and Saudi Arabia, covering a period between 2000 and 2022. The results undermine the general notion that the usage of available multi-factor asset-pricing models automatically yields meaningful data in all economic situations. The study reiterates the need to reconsider the assumption that the addition of more company-specific factors to regression models automatically yields better results. This study contributes to the existing literature by broadening this research area. It is the first study to specifically analyze the performance of companies from the energy sector in a crisis like the COVID-19 pandemic with the help of the Fama-French three- and five-factor models. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

9 pages, 642 KiB

Open AccessArticle

Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos

by Melike Bildirici, Yasemen Ucan and Sérgio Lousada

Mathematics 2022, 10(21), 3998; https://doi.org/10.3390/math10213998 - 27 Oct 2022

Cited by 1 | Viewed by 1016

Abstract

This paper aims to test the structure of interest rates during the period from 1 September 1981 to 28 December 2020 by using Lie algebras and groups. The selected period experienced substantial events impacting interest rates, such as the economic crisis, the military intervention of the USA in Iraq, and the COVID-19 pandemic, in which economies were in lockdown. These conditions caused the interest rate to have a nonlinear structure, chaotic behavior, and outliers. Under these conditions, an alternative method is proposed to test the random and nonlinear structure of interest rates to be evolved by a stochastic differential equation captured on a curved state space based on Lie algebras and group. Then, parameter estimates of this equation were obtained by OLS, NLS, and GMM estimators (hereafter, Lie_NLS, Lie_OLS, and Lie_GMM, respectively). Therefore, the interest rates that possess nonlinear structures and/or chaotic behaviors or outliers were tested with Lie_NLS, Lie_OLS, and Lie_GMM. We compared our Lie_NLS, Lie_OLS, and Lie_GMM results with the traditional OLS, NLS, and GMM methods, and the results favor the improvement achieved by the proposed Lie_NLS, Lie_OLS, and Lie_GMM in terms of the RMSE and MAE in the out-of-sample forecasts. Lastly, the Lie algebras with NLS estimators exhibited the lowest RMSE and MAE followed by the Lie algebras with GMM, and the Lie algebras with OLS, respectively. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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17 pages, 2539 KiB

Open AccessArticle

Support Resistance Levels towards Profitability in Intelligent Algorithmic Trading Models

by Jireh Yi-Le Chan, Seuk Wai Phoong, Wai Khuen Cheng and Yen-Lin Chen

Mathematics 2022, 10(20), 3888; https://doi.org/10.3390/math10203888 - 20 Oct 2022

Viewed by 3730

Abstract

Past studies showed that more advanced model architectures and techniques are being developed for intelligent algorithm trading, but the input features of the models across these studies are very similar. This justifies the increasing need for new meaningful input features to better explain price movements. This study shows that the inclusion of Support Resistance input features engineered from the proposed novel methodology increased the machine learning model’s aggregate profitability performance by 65% across eight currency pairs when compared to an identical machine learning model without the Support Resistance input features. Moreover, the results also showed that the profitability distribution is statistically significantly different between two identical intelligent models with and without the Support Resistance input features, respectively. Therefore, the objective of this study is 3-fold: (1) to propose a novel methodology to automate meaningful Support Resistance price levels identification; (2) to propose a methodology to engineer Support Resistance features for Machine Learning Models to improve algorithmic trading profitability; (3) to provide empirical evidence towards the significant incremental contribution of Support Resistance (Psychological Price Levels) input features towards profitability in algorithmic trading models. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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11 pages, 275 KiB

Open AccessFeature PaperArticle

A Game Theoretic Model of Struggle with Corruption in Auctions: Computer Simulation

by Kirill Kozlov and Guennady Ougolnitsky

Mathematics 2022, 10(19), 3653; https://doi.org/10.3390/math10193653 - 05 Oct 2022

Cited by 1 | Viewed by 1033

Abstract

There is a great deal of literature devoted to mathematical models of corruption, including corruption in auctions. However, the relationship between the seller and the auctioneer is not studied sufficiently. The research aim is to analyze such relations in a game theoretic setup. We built a difference game theoretic model in normal form that describes possible collusion between an auctioneer and participants of an auction. The auctioneer acts on behalf of a seller. The seller can control possible collusions by administrative and economic mechanisms. The probability of detection depends on audit cost. We consider four cases of absence/presence of the collusion and those of the audit. The model is investigated numerically by simulation modeling using an original method of qualitatively representative scenarios. Several conclusions are made: factors of corruption are low probability of detection, small penalty, and big corruption gain of the auctioneer. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

15 pages, 1071 KiB

Open AccessArticle

A Mixed-Integer Program for Drawing Orthogonal Hyperedges in a Hierarchical Hypergraph

by Gregory Fridman, Yuri Vasiliev, Vlada Puhkalo and Vladimir Ryzhov

Mathematics 2022, 10(5), 689; https://doi.org/10.3390/math10050689 - 23 Feb 2022

Cited by 3 | Viewed by 1381

Abstract

This paper presents a new formulation and solution of a mixed-integer program for the hierarchical orthogonal hypergraph drawing problem, and the number of hyperedge crossings is minimized. The novel feature of the model is in combining several stages of the Sugiyama framework for graph drawing: vertex ordering, the assignment of vertices’ x-coordinates, and orthogonal hyperedge routing. The hyperedges of a hypergraph are assumed to be multi-source and multi-target, and vertices are depicted as rectangles with ports on their top and bottom sides. Such hypergraphs are used in data-flow diagrams and in a scheme of cooperation. The numerical results demonstrate the correctness and effectiveness of the proposed approach compared to mathematical heuristics. For instance, the proposed exact approach yields a

67.3 %

reduction of the number of crossings compared to that obtained by using a mathematical heuristic for a dataset of non-planar graphs. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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16 pages, 307 KiB

Open AccessArticle

An Analysis and Comparison of Multi-Factor Asset Pricing Model Performance during Pandemic Situations in Developed and Emerging Markets

by Konstantin B. Kostin, Philippe Runge and Michel Charifzadeh

Mathematics 2022, 10(1), 142; https://doi.org/10.3390/math10010142 - 04 Jan 2022

Cited by 6 | Viewed by 3370

Abstract

This study empirically analyzes and compares return data from developed and emerging market data based on the Fama French five-factor model and compares it to previous results from the Fama French three-factor model by Kostin, Runge and Adams (2021). It researches whether the addition of the profitability and investment pattern factors show superior results in the assessment of emerging markets during the COVID-19 pandemic compared to developed markets. We use panel data covering eight indices of developed and emerging countries as well as a selection of eight companies from these markets, covering a period from 2000 to 2020. Our findings suggest that emerging markets do not generally outperform developed markets. The results underscore the need to reconsider the assumption that adding more factors to regression models automatically yields results that are more reliable. Our study contributes to the extant literature by broadening this research area. It is the first study to compare the performance of the Fama French three-factor model and the Fama French five-factor model in the cost of equity calculation for developed and emerging countries during the COVID-19 pandemic and other crisis events of the past two decades. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

17 pages, 341 KiB

Open AccessArticle

A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

by Chen Mao, Guanqi Liu and Yuwen Wang

Mathematics 2022, 10(1), 5; https://doi.org/10.3390/math10010005 - 21 Dec 2021

Cited by 3 | Viewed by 2374

Abstract

At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and

It \hat{o}

’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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20 pages, 2112 KiB

Open AccessEditor’s ChoiceArticle

Deep Learning Models for Predicting Monthly TAIEX to Support Making Decisions in Index Futures Trading

by Duy-An Ha, Chia-Hung Liao, Kai-Shien Tan and Shyan-Ming Yuan

Mathematics 2021, 9(24), 3268; https://doi.org/10.3390/math9243268 - 16 Dec 2021

Cited by 2 | Viewed by 4094

Abstract

Futures markets offer investors many attractive advantages, including high leverage, high liquidity, fair, and fast returns. Highly leveraged positions and big contract sizes, on the other hand, expose investors to the risk of massive losses from even minor market changes. Among the numerous stock market forecasting tools, deep learning has recently emerged as a favorite tool in the research community. This study presents an approach for applying deep learning models to predict the monthly average of the Taiwan Capitalization Weighted Stock Index (TAIEX) to support decision-making in trading Mini-TAIEX futures (MTX). We inspected many global financial and economic factors to find the most valuable predictor variables for the TAIEX, and we examined three different deep learning architectures for building prediction models. A simulation on trading MTX was then performed with a simple trading strategy and two different stop-loss strategies to show the effectiveness of the models. We found that the Temporal Convolutional Network (TCN) performed better than other models, including the two baselines, i.e., linear regression and extreme gradient boosting. Moreover, stop-loss strategies are necessary, and a simple one could be sufficient to reduce a severe loss effectively. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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13 pages, 49646 KiB

Open AccessArticle

Complex Investigations of a Piecewise-Smooth Remanufacturing Bertrand Duopoly Game

by Sameh Askar

Mathematics 2021, 9(20), 2558; https://doi.org/10.3390/math9202558 - 13 Oct 2021

Viewed by 1148

Abstract

This paper considers a Bertrand competition between two firms whose decision variables are derived from a quadratic utility function. The first firm produces new products with their own prices while the second firm re-manufactures returned products and sells them in the market at prices that may be less than or equal to the price of the first firm. Dynamically, this competition is constructed on which boundedly rational firms apply a gradient adjustment mechanism to update their prices in each period. According to this mechanism and the nature of the competition, a two-dimensional piecewise smooth discrete dynamic map was constructed in order to study the complex dynamic characteristics of the game. The phase plane of the map was divided into two different regions, separated by border curve. The equilibrium points of the map, in each region on where they are defined, were calculated, and their stability conditions were investigated. Furthermore, we conducted a global analysis to investigate the complex structure of the map, such as closed invariant curves, periodic cycles, and chaotic attractors and their basins, which cause qualitative changes as some parameters are allowed to vary. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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18 pages, 2400 KiB

Open AccessEditor’s ChoiceArticle

Revisiting the Valuable Roles of Global Financial Assets for International Stock Markets: Quantile Coherence and Causality-in-Quantiles Approaches

by Zhenghui Li, Zhiming Ao and Bin Mo

Mathematics 2021, 9(15), 1750; https://doi.org/10.3390/math9151750 - 24 Jul 2021

Cited by 36 | Viewed by 2762

Abstract

We employ the quantile-coherency approach and causality-in-quantile method to revisit the roles of Bitcoin, U.S. dollar, crude oil and gold for USA, Chinese, UK, and Japanese stock markets. The main results show that the impact of global financial assets varies across different investment horizons and quantiles. We find that in most cases, the correlation between global financial assets and stock indexes is not significant or is weakly positive. From the perspective of investment horizons (frequency domain), the correlation in the short term is mostly manifested in Bitcoin, while in the medium and long term it is shifted to dollar assets. At the same time, the relationships are significantly higher in the medium and long term than in the short term. From the point of view of quantiles, it shows a weak positive correlation at the lower quantile. However, the correlation between the two is not significant at the median quantile. At the high quantiles, there is a weak negative linkage. According to the causality-in-quantiles approach results, in most cases global financial assets have different degrees of predictive capacity for the selected stock markets. Especially around the median quantile, the predictive ability was strongest. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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11 pages, 1546 KiB

Open AccessArticle

Formation of the Entrepreneurial Potential of Student Youth: A Factor of Work Experience

by Nataliya Chukhray, Michal Greguš, Oleh Karyy and Liubov Halkiv

Mathematics 2021, 9(13), 1494; https://doi.org/10.3390/math9131494 - 25 Jun 2021

Cited by 2 | Viewed by 1564

Abstract

International norms regarding educational activity are aimed at forming entrepreneurial competencies in students. The motivational readiness of student youth to implement these entrepreneurial competencies in practice reflects the potential for entrepreneurship development. Despite the social group of student youths being considered belonging to the category of economically inactive population, students are traditionally engaged in social production. New changes in labor and consumption conditions of higher education services contribute to the growing trend in students who combine study and work. Considering this trend, we investigate the impact of students’ work experience on forming their entrepreneurial potential. The analytical component of this study is performed according to the materials obtained through a questionnaire, which covers 746 students. The findings prove that students who engage in employment before studying at university tended to combine university studies and employment in social production. Having such an employment experience increases students’ confidence regarding their entrepreneurial abilities and has a positive effect on students’ intentions to start their own businesses. Simultaneously, the lack of experience in management assistance does not constrain students’ intentions to start a business. Full article

(This article belongs to the Special Issue Mathematics and Financial Economics)

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