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Mathematics
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Computational Economics and Mathematical Modeling
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Computational Economics and Mathematical Modeling

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

Deadline for manuscript submissions: 31 January 2025 | Viewed by 9713

Special Issue Editors

Prof. Dr. Yi-Hsien Wang

E-Mail Website
Guest Editor
Doctorate Program in Intelligent Banking and Finance, CTBC Business School, Tainan 709, Taiwan
Interests: financial econometrics; investment management; decision science; risk analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Chien-Ming Huang

E-Mail Website
Guest Editor
Department of Banking and Finance, Tamkang University, New Taipei City 251301, Taiwan
Interests: quantitative finance; financial econometrics; mathematical modeling; risk management

Special Issue Information

Dear Colleagues,

In order to improve corporate competitiveness, academia has remained nimble and adaptable and has continued to expand and advance academic research in emerging fields such as corporate innovation and big data analytics in the last few decades. Therefore, related models such as applied computational economics and numerical analysis of mathematical modeling have attracted great attention from academia and industry. From a broad quantitative perspective, enterprises conduct mathematical modeling, numerical analysis, data simulation, statistical estimation and sensitivity analysis through mathematical analysis models such as computational economics, quantitative models, big data analysis, machine learning, decision science analysis and statistical models to assist the business analysis and decision-making management of enterprises. This Special Issue aims to encourage and collect relevant research papers that apply models such as computational economics and mathematical modeling to improve and support current research methods in the field of economic behavior and decision-making. 

Prof. Dr. Yi-Hsien Wang
Dr. Chien-Ming Huang
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • computational economics
  • quantitative model
  • mathematical modeling
  • big data analysis
  • econometrics
  • machine learning
  • statistical model
  • decision science analysis

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Published Papers (5 papers)

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Research

22 pages, 496 KiB  
Article
Three-Layer Artificial Neural Network for Pricing Multi-Asset European Option
by Zhiqiang Zhou, Hongying Wu, Yuezhang Li, Caijuan Kang and You Wu
Mathematics 2024, 12(17), 2770; https://doi.org/10.3390/math12172770 - 7 Sep 2024
Viewed by 589
Abstract
This paper studies an artificial neural network (ANN) for multi-asset European options. Firstly, a simple three-layer ANN-3 is established with undetermined weights and bias. Secondly, the time–space discrete PDE of the multi-asset option is given and the corresponding discrete data are fed into [...] Read more.
This paper studies an artificial neural network (ANN) for multi-asset European options. Firstly, a simple three-layer ANN-3 is established with undetermined weights and bias. Secondly, the time–space discrete PDE of the multi-asset option is given and the corresponding discrete data are fed into the ANN-3. Then, using least squares error as the objective function, the weights and bias of ANN-3 are trained well. Numerical examples are carried out to confirm the stability, accuracy and efficiency. Experiments show the ANN’s relative error is about 0.8%. This method can be extended into multi-layer ANN-q(q>3) and extended into American options. Full article
(This article belongs to the Special Issue Computational Economics and Mathematical Modeling)
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19 pages, 2102 KiB  
Article
Evaluating the Efficiency of Financial Assets as Hedges against Bitcoin Risk during the COVID-19 Pandemic
by Li Wei, Ming-Chih Lee, Wan-Hsiu Cheng, Chia-Hsien Tang and Jing-Wun You
Mathematics 2023, 11(13), 2917; https://doi.org/10.3390/math11132917 - 29 Jun 2023
Cited by 5 | Viewed by 1745
Abstract
In the turbulent landscape of financial markets, Bitcoin has emerged as a significant focus for investors due to its highly volatile returns. However, the risks and uncertainties associated with it necessitate effective hedging strategies. This paper explores the potential of various financial assets, [...] Read more.
In the turbulent landscape of financial markets, Bitcoin has emerged as a significant focus for investors due to its highly volatile returns. However, the risks and uncertainties associated with it necessitate effective hedging strategies. This paper explores the potential of various financial assets, including interest rates, stock markets, commodities, and exchange rates, as dynamic hedges against Bitcoin’s risk. Utilizing a DCC-GARCH model, we construct a dynamic hedging model to analyze the viability of these financial assets as hedges. The data is categorized into pre-pandemic and pandemic periods to assess any change in hedging performance due to the outbreak of COVID-19. Our empirical findings suggest that the dynamic DCC-GARCH model outperforms the static OLS model in this context. During the pandemic period, a diverse set of financial assets demonstrated enhanced efficiency in hedging Bitcoin risk compared to the pre-pandemic phase. Among the hedging commodities, stock market indices, the US dollar index, and commodity futures displayed superior performance. Full article
(This article belongs to the Special Issue Computational Economics and Mathematical Modeling)
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16 pages, 2862 KiB  
Article
Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning
by Xiangdong Liu and Yu Gu
Mathematics 2023, 11(12), 2658; https://doi.org/10.3390/math11122658 - 11 Jun 2023
Cited by 1 | Viewed by 1724
Abstract
Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, [...] Read more.
Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDEs) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function, and they are approximated, respectively, by using two multilayer neural networks as function approximators. Thus, the deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and option pricing under the jump diffusion model. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields. Full article
(This article belongs to the Special Issue Computational Economics and Mathematical Modeling)
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15 pages, 1554 KiB  
Article
Does ESG Predict Systemic Banking Crises? A Computational Economics Model of Early Warning Systems with Interpretable Multi-Variable LSTM based on Mixture Attention
by Shu-Ling Lin and Xiao Jin
Mathematics 2023, 11(2), 410; https://doi.org/10.3390/math11020410 - 12 Jan 2023
Cited by 4 | Viewed by 2619
Abstract
Systemic banking crises can be very damaging to economic development, and environmental, social, and governance (ESG) can also damage national finances, but there is no research on whether ESG affects systemic banking crises, and we fill this gap. We first employ Fisher scores [...] Read more.
Systemic banking crises can be very damaging to economic development, and environmental, social, and governance (ESG) can also damage national finances, but there is no research on whether ESG affects systemic banking crises, and we fill this gap. We first employ Fisher scores (FS) to select features and then use an interpretable multivariate long-short-term memory (IMV-LSTM) model with focal loss (FL) to account for class imbalance to model an early warning system (EWS) that can predict up to one year in advance. This study finds that ESG influences the occurrence of systemic banking crises, with our early warning system predicting each crisis a year in advance. Full article
(This article belongs to the Special Issue Computational Economics and Mathematical Modeling)
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17 pages, 472 KiB  
Article
The Valuation of Contract Deposit and Purchase Price
by Chien-Ming Huang and Ta-Cheng Chang
Mathematics 2022, 10(23), 4535; https://doi.org/10.3390/math10234535 - 30 Nov 2022
Cited by 1 | Viewed by 1524
Abstract
This paper evaluates the deposit and purchase pricing of purchase contracts in a risk-neutral framework. First, we determine the fair deposit price of a single-installment purchase contract based on theoretical modeling and numerical analysis. Second, the buyer’s threshold pricing in dual-installment and multi-installment [...] Read more.
This paper evaluates the deposit and purchase pricing of purchase contracts in a risk-neutral framework. First, we determine the fair deposit price of a single-installment purchase contract based on theoretical modeling and numerical analysis. Second, the buyer’s threshold pricing in dual-installment and multi-installment contracts is investigated under the framework of compound options. Lastly, the pricing behavior of deposits and purchases is further analyzed using a simultaneous equations modeling framework. Full article
(This article belongs to the Special Issue Computational Economics and Mathematical Modeling)
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