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Mathematics
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Mathematical Models and Applications in Finance
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Mathematical Models and Applications in Finance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: closed (30 November 2024) | Viewed by 10254

Special Issue Editors

Dr. Rand Low

E-Mail Website
Guest Editor
1. Associate Professor, Bond Business School, Bond University, Robina, QLD 4226, Australia
2. Honorary Senior Fellow, UQ Business School, University of Queensland, St Lucia, QLD, Australia
Interests: portfolio optimization; market risk; dependence modelling; copulas; pairs trading
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yasuaki Watanabe

E-Mail Website
Guest Editor
Department of Business and Marketing Strategy Professor, Kindai University, Higashiosaka, Osaka 577-8502, Japan
Interests: pension funds; asset allocation; corporate finance

Special Issue Information

Dear colleagues,

In financial research, mathematical modelling allows for the establishment of a functional relationship between multiple variables, thereby being an effective method with which to analyse and solve problems in financial economics. Mathematical models underpin our understanding of many problems in financial economics, ranging from Markowitz’s (1952) mean-variance optimisation, which underpins modern portfolio theory (MPT), to the Black–Scholes–Merton model for option pricing and the Black–Litterman model, which incorporates investors’ views of expected returns in MPT. Advancements in the fields of statistical and machine learning have led towards uses in the areas of credit risk and asset pricing. In this context, we are seeking to publish high-quality research on fund management, risk management (i.e., credit, market, and operational), portfolio optimisation, asset pricing, option pricing, volatility spillovers, and any other topics related to mathematical finance. We pay particular attention to the importance of the use of big data and AI/ML techniques in financial economics. We encourage the submission of quantitative research works.

Dr. Rand Low
Prof. Dr. Yasuaki Watanabe
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

  • portfolio optimisation
  • asset pricing
  • credit risk
  • market risk
  • fund management
  • interest rates
  • operational risk
  • fixed income
  • commodities
  • equities
  • cryptocurrency
  • volatility modelling
  • spillovers
  • derivatives
  • factor models

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Published Papers (5 papers)

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Research

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14 pages, 3157 KiB  
Article
An Advanced Time-Varying Capital Asset Pricing Model via Heterogeneous Autoregressive Framework: Evidence from the Chinese Stock Market
by Bohan Zhao, Hong Yin and Yonghong Long
Mathematics 2025, 13(1), 41; https://doi.org/10.3390/math13010041 - 26 Dec 2024
Viewed by 696
Abstract
The capital asset pricing model (CAPM) is a foundational asset pricing model that is widely applied and holds particular significance in the globally influential Chinese stock market. This study focuses on the banking sector, enhancing the performance of the CAPM and further assessing [...] Read more.
The capital asset pricing model (CAPM) is a foundational asset pricing model that is widely applied and holds particular significance in the globally influential Chinese stock market. This study focuses on the banking sector, enhancing the performance of the CAPM and further assessing its applicability within the Chinese stock market context. This study incorporates a heterogeneous autoregressive (HAR) component into the CAPM framework, developing a CAPM-HAR model with time-varying beta coefficients. Empirical analysis based on high-frequency data demonstrates that the CAPM-HAR model not only enhances the capability of capturing market fluctuations but also significantly improves its applicability and predictive accuracy for stocks in the Chinese banking sector. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Finance)
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19 pages, 636 KiB  
Article
Analytical Shortcuts to Multiple-Objective Portfolio Optimization: Investigating the Non-Negativeness of Portfolio Weight Vectors of Equality-Constraint-Only Models and Implications for Capital Asset Pricing Models
by Yue Qi, Yue Wang, Jianing Huang and Yushu Zhang
Mathematics 2024, 12(24), 3946; https://doi.org/10.3390/math12243946 - 15 Dec 2024
Viewed by 891
Abstract
Computing optimal-solution sets has long been a topic in multiple-objective optimization. Despite substantial progress, there are still research limitations in the multiple-objective portfolio optimization area. The optimal-solution sets’ structure is barely known. Public-domain software for even three objectives is absent. Alternatively, researchers scrutinize [...] Read more.
Computing optimal-solution sets has long been a topic in multiple-objective optimization. Despite substantial progress, there are still research limitations in the multiple-objective portfolio optimization area. The optimal-solution sets’ structure is barely known. Public-domain software for even three objectives is absent. Alternatively, researchers scrutinize equality-constraint-only models and analytically resolve them. Within this context, this paper extends these analytical methods for nonnegative constraints and thus theoretically contributes to the literature. We prove the existence of positive elements and negative elements for the optimal-solution sets. Practically, we prove that non-negative subsets of the optimal-solution sets can exist. Consequently, the possible existence endorses these analytical methods, because researchers bypass mathematical programming, analytically resolve, and pinpoint some non-negative optima. Moreover, we elucidate these analytical methods’ alignment with capital asset pricing models (CAPMs). Furthermore, we generalize for k-objective models. In conclusion, this paper theoretically reinforces these analytical methods and hints the optimal-solution sets’ structure for multiple-objective portfolio optimization. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Finance)
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9 pages, 317 KiB  
Article
Kelly Criterion Extension: Advanced Gambling Strategy
by Song-Kyoo (Amang) Kim
Mathematics 2024, 12(11), 1725; https://doi.org/10.3390/math12111725 - 1 Jun 2024
Cited by 1 | Viewed by 2999
Abstract
This article introduces an innovative extension of the Kelly criterion, which has traditionally been used in gambling, sports wagering, and investment contexts. The Kelly criterion extension (KCE) refines the traditional capital growth function to better suit dynamic market conditions. The KCE improves the [...] Read more.
This article introduces an innovative extension of the Kelly criterion, which has traditionally been used in gambling, sports wagering, and investment contexts. The Kelly criterion extension (KCE) refines the traditional capital growth function to better suit dynamic market conditions. The KCE improves the traditional approach to accommodate the complexities of financial markets, particularly in stock and commodity trading. This innovative method focuses on crafting strategies based on market conditions and player actions rather than direct asset investments, which enhances its practical application by minimizing risks associated with volatile investments. This paper is structured to first outline the foundational concepts of the Kelly criterion, followed by a detailed presentation of the KCE and its advantages in practical scenarios, including a case study on its application to blackjack strategy optimization. The mathematical framework and real-world applicability of the KCE are thoroughly discussed, demonstrating its potential to bridge the gap between theoretical finance and actual trading outcomes. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Finance)
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31 pages, 12380 KiB  
Article
Systemic Financial Risk Forecasting: A Novel Approach with IGSA-RBFNN
by Yishuai Tian and Yifan Wu
Mathematics 2024, 12(11), 1610; https://doi.org/10.3390/math12111610 - 21 May 2024
Cited by 2 | Viewed by 1670
Abstract
Accurate measurement of systemic financial risk is crucial for maintaining the stability of financial markets. Taking China as the subject of investigation, the Chinese Financial Stress Index (CFSI) indicator system was constructed by integrating six dimensions and employing Gray Relation Analysis (GRA) to [...] Read more.
Accurate measurement of systemic financial risk is crucial for maintaining the stability of financial markets. Taking China as the subject of investigation, the Chinese Financial Stress Index (CFSI) indicator system was constructed by integrating six dimensions and employing Gray Relation Analysis (GRA) to reduce the dimensionality of the indicators. The CFSI was derived using the Attribute Hierarchy Model (AHM) method with the Criteria Importance Through the Intercriteria Correlation (CRITIC) method, and an Improved Gravitational Search Algorithm (IGSA)-optimized Radial Basis Function Neural Network (RBFNN) was proposed for out-of-sample prediction of CFSI trends from 2024 to 2026. By analyzing the trends in financial pressure indicators, the intricate relationship between financial pressure and economic activity can be effectively discerned. The research findings indicate that (1) the CFSI is capable of accurately reflecting the current financial stress situation in China, and (2) the IGSA-RBFNN demonstrates strong robustness and generalization capabilities, predicting that the CFSI index will reach a peak value of 0.543 by the end of 2024, and there exists a regular pattern of stress rebound towards the end of each year. The novel methodology enables policymakers and regulatory authorities to proactively identify potential risks and vulnerabilities, facilitating the formulation of preventive measures. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Finance)
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Review

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25 pages, 6951 KiB  
Review
Quantitative Portfolio Management: Review and Outlook
by Michael Senescall and Rand Kwong Yew Low
Mathematics 2024, 12(18), 2897; https://doi.org/10.3390/math12182897 - 17 Sep 2024
Viewed by 2847
Abstract
This survey aims to provide insightful and objective perspectives on the research history of quantitative portfolio management strategies with suggestions for the future of research. The relevant literature can be clustered into four broad themes: portfolio optimization, risk-parity, style integration, and machine learning. [...] Read more.
This survey aims to provide insightful and objective perspectives on the research history of quantitative portfolio management strategies with suggestions for the future of research. The relevant literature can be clustered into four broad themes: portfolio optimization, risk-parity, style integration, and machine learning. Portfolio optimization attempts to find the optimal trade-off of future returns per unit of risk. Risk-parity attempts to match the exposure of various asset classes such that no single asset class dominates portfolio risk. Style integration combines risk factors on a security level such that rebalancing differences cancel out. Finally, machine learning utilizes large arrays of tunable parameters to predict future asset behavior and solve non-convex optimization problems. We conclude that machine learning will likely be the focus of future research. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Finance)
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