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Axioms
Special Issues
Mathematical and Computational Finance Analysis
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Mathematical and Computational Finance Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (26 January 2024) | Viewed by 16351

Special Issue Editors

Prof. Dr. Irina Arhipova

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Guest Editor
Faculty of Information Technologies, Latvia University of Life Sciences and Technologies, LV 3001 Jelgava, Latvia
Interests: econometrics and its applications; risk management methods; decision-making support systems
Dr. Mitra Arami

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Guest Editor
Métis Lab, EM Normandie Business School, 76600 Le Havre, France
Interests: Fintech, payment services, project management; business excellence and maturity models; digital transformation, diffusion of innovations; as well as AI and machine learning
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Signe Balina

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Guest Editor
Faculty of Business, Management and Economics, University of Latvia, LV 1050 Riga, Latvia
Interests: digital transformation; e-commerce; data analysis; econometrics; AI and machine learning
Prof. Dr. Victor Chang

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Guest Editor
Department of Operations and Information Management, Aston Business School, Aston University, Birmingham B4 7ET, UK
Interests: Internet of Things; big data; industry 4.0; security/risk and cloud/edge/fog computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will focus on the broad topics of "Mathematical and Computational Finance analysis", presenting original research on the application of mathematical and machine learning techniques for modeling in finance. Modern finance is currently characterized by the necessity to find optimal solutions to business and investment decisions in the face of uncertainty and in the context of the consequences of the COVID-19 pandemic. Mathematical and computational finance analysis are complementary areas that provide real-world problem solving with the theoretical and applied application of algorithms and methods, where machine learning techniques for processing and analyzing real financial data allow solving major financial issues in the financial industry.

The aim of this Special Issue is to report the latest progress in the theory of modern finance to real-world settings and make relevant case studies. Original research articles and reviews are welcome that address one or more of the following problems: financial risk management, mathematical and statistical finance modeling, numerical methods, decision making, optimization, financial applications, stochastic time-series modeling, financial computation and modeling, and applications of computational finance. Topics of interest include but are not limited to the issues presented. We look forward to receiving your contributions.

Prof. Dr. Irina Arhipova
Dr. Mitra Arami
Prof. Dr. Signe Balina
Prof. Dr. Victor Chang
Guest Editors

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.

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. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • financial data analysis
  • computation
  • computing and financial management
  • machine learning for finance
  • mathematical finance
  • mathematical and statistical modeling

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Published Papers (5 papers)

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Research

22 pages, 2619 KiB  
Article
Forecasting the S&P 500 Index Using Mathematical-Based Sentiment Analysis and Deep Learning Models: A FinBERT Transformer Model and LSTM
by Jihwan Kim, Hui-Sang Kim and Sun-Yong Choi
Axioms 2023, 12(9), 835; https://doi.org/10.3390/axioms12090835 - 29 Aug 2023
Cited by 12 | Viewed by 7472
Abstract
Stock price prediction has been a subject of significant interest in the financial mathematics field. Recently, interest in natural language processing models has increased, and among them, transformer models, such as BERT and FinBERT, are attracting attention. This study uses a mathematical framework [...] Read more.
Stock price prediction has been a subject of significant interest in the financial mathematics field. Recently, interest in natural language processing models has increased, and among them, transformer models, such as BERT and FinBERT, are attracting attention. This study uses a mathematical framework to investigate the effects of human sentiment on stock movements, especially in text data. In particular, FinBERT, a domain-specific language model based on BERT tailored for financial language, was employed for the sentiment analysis on the financial texts to extract sentiment information. In this study, we use “summary” text data extracted from The New York Times, representing concise summaries of news articles. Accordingly, we apply FinBERT to the summary text data to calculate sentiment scores. In addition, we employ the LSTM (Long short-term memory) methodology, one of the machine learning models, for stock price prediction using sentiment scores. Furthermore, the LSTM model was trained by stock price data and the estimated sentiment scores. We compared the predictive power of LSTM models with and without sentiment analysis based on error measures such as MSE, RMSE, and MAE. The empirical results demonstrated that including sentiment scores through the LSTM model led to improved prediction accuracy for all three measures. These findings indicate the significance of incorporating news sentiment into stock price predictions, shedding light on the potential impact of psychological factors on financial markets. By using the FinBERT transformer model, this study aimed to investigate the interplay between sentiment and stock price predictions, contributing to a deeper understanding of mathematical-based sentiment analysis in finance and its role in enhancing forecasting in financial mathematics. Furthermore, we show that using summary data instead of entire news articles is a useful strategy for mathematical-based sentiment analysis. Full article
(This article belongs to the Special Issue Mathematical and Computational Finance Analysis)
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11 pages, 254 KiB  
Article
A Lower Bound for the Volatility Swap in the Lognormal SABR Model
by Elisa Alòs, Frido Rolloos and Kenichiro Shiraya
Axioms 2023, 12(8), 749; https://doi.org/10.3390/axioms12080749 - 29 Jul 2023
Viewed by 1252
Abstract
In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and [...] Read more.
In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and is a sharper lower bound than the at-the-money implied volatility for correlation less than or equal to zero. Full article
(This article belongs to the Special Issue Mathematical and Computational Finance Analysis)
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25 pages, 963 KiB  
Article
An Equilibrium Strategy for Target Benefit Pension Plans with a Longevity Trend and Partial Information
by Wei Liu, Na Li and Ahmadjan Muhammadhaji
Axioms 2023, 12(8), 732; https://doi.org/10.3390/axioms12080732 - 27 Jul 2023
Viewed by 1326
Abstract
This paper considers the problem of portfolio selection and adjustment for target benefit plans (TBP) with longevity trends and partial information. The longevity trends are modeled by a time-varying force function. The financial market consists of risk-free assets and stocks, in which the [...] Read more.
This paper considers the problem of portfolio selection and adjustment for target benefit plans (TBP) with longevity trends and partial information. The longevity trends are modeled by a time-varying force function. The financial market consists of risk-free assets and stocks, in which the return rate of stocks is a stochastic process and cannot be completely observed. This paper adopts the mean-variance utility model as an optimization criterion. The aim is to maximize the terminal value of the pension fund and the excess pension benefit after the participant’s retirement. The optimization equations are developed in game theory to obtain explicit solutions for the equilibrium strategies. Finally, the influence of the longevity trend on the internal structure of the pension system and the sensitivity of the equilibrium strategies to the related parameters are explored by numerical analysis. The conclusion shows that this model’s results can provide stable and adequate retirement benefits for participants. Full article
(This article belongs to the Special Issue Mathematical and Computational Finance Analysis)
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28 pages, 14154 KiB  
Article
Uncovering the Impact of Local and Global Interests in Artists on Stock Prices of K-Pop Entertainment Companies: A SHAP-XGBoost Analysis
by Daeun Yu and Sun-Yong Choi
Axioms 2023, 12(6), 538; https://doi.org/10.3390/axioms12060538 - 30 May 2023
Viewed by 3709
Abstract
Stock price prediction is a significant area of research in finance that has been ongoing for a long time. Several mathematical models have been utilized in this field to predict stock prices. However, recently, machine learning techniques have demonstrated remarkable performance in stock [...] Read more.
Stock price prediction is a significant area of research in finance that has been ongoing for a long time. Several mathematical models have been utilized in this field to predict stock prices. However, recently, machine learning techniques have demonstrated remarkable performance in stock price prediction. Moreover, XAI (explainable artificial intelligence) methodologies have been developed, which are models capable of interpreting the results of machine learning algorithms. This study utilizes machine learning to predict stock prices and uses XAI methodologies to investigate the factors that influence this prediction. Specifically, we investigated the relationship between the public’s interest in artists affiliated with four K-Pop entertainment companies (HYBE, SM, JYP, and YG). We used the Naver Keyword Trend and Google Trend index data for the companies and their representative artists to measure local and global interest. Furthermore, we employed the SHAP-XGBoost model to show how the local and global interest in each artist affects the companies’ stock prices. SHAP (SHapley Additive exPlanations) and XGBoost are models that show excellent results as XAI and machine learning methodologies, respectively. We found that SM, JYP, and YG are highly correlated, whereas HYBE is a major player in the industry. YG is influenced by variables from other companies, likely owing to HYBE being a major shareholder in YG’s subsidiary music distribution company. The influence of popular artists from each company was significant in predicting the companies’ stock prices. Additionally, the foreign ownership ratio of a company’s stocks affected the importance of Google Trend and Naver Trend indexes. For example, JYP and SM had relatively high foreign ownership ratios and were influenced more by Google Trend indexes, whereas HYBE and YG were influenced more by Naver Trend indexes. Finally, the trend indexes of artists in SM and HYBE had a positive correlation with stock prices, whereas those of YG and JYP had a negative correlation. This may be due to steady promotions and album releases from SM and HYBE artists, while YG and JYP suffered from negative publicity related to their artists and executives. Overall, this study suggests that public interest in K-Pop artists can have a significant impact on the financial performance of entertainment companies. Moreover, our approach offers valuable insights into the dynamics of the stock market, which makes it a promising technique for understanding and predicting the behavior of entertainment stocks. Full article
(This article belongs to the Special Issue Mathematical and Computational Finance Analysis)
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8 pages, 265 KiB  
Article
Non-Parametric Regression and Riesz Estimators
by Christos Kountzakis and Vasileia Tsachouridou-Papadatou
Axioms 2023, 12(4), 375; https://doi.org/10.3390/axioms12040375 - 14 Apr 2023
Cited by 1 | Viewed by 1311
Abstract
In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis [...] Read more.
In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis elements of the finite-dimensional sub-lattice generated by the rows of some design matrix. A strong motivation for using the Riesz estimator model is that the data of explanatory variables may come from categorical variables. Calculations related to Riesz estimator regression are very easy since they arise from the measurability in finite-dimensional probability spaces. Moreover, we show that the fitted model of Riesz estimators is an ordinary least squares model. Any vector of some Euclidean space is supposed to be a rendom variable under the objective probability values, being used in expected utility theory and its applications. Finally, the reader may notice that goodness-of-fit measures are similar to those defined for the usual linear regression. Due to the fact that this model is non-parametric, it may include samples relevant to finance and actuarial science variables. Full article
(This article belongs to the Special Issue Mathematical and Computational Finance Analysis)
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