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Axioms
Special Issues
Advances in Financial Mathematics
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Advances in Financial Mathematics

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 28 February 2025 | Viewed by 8299

Special Issue Editors

Prof. Dr. Conghua Wen

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Guest Editor
School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University, Suzhou, China
Interests: stochastic process; numerical solutions on stochastic models; model estimation and model selection
Special Issues, Collections and Topics in MDPI journals
Dr. Yi Hong

E-Mail Website
Guest Editor
Department of Financial and Actuarial Mathematics, Xi'an Jiaotong-Liverpool University, Suzhou, China
Interests: quantitative finance; mathematical modelling
Dr. Xianming Sun

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Guest Editor
School of Finance, Zhongnan University of Economics and Law, Wuhan, China
Interests: financial mathematics; financial engineering
Prof. Dr. Fei Ma

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Guest Editor
Applied Mathematics, Xi'an Jiaotong-Liverpool University, Suzhou, China
Interests: patten recognition; quantative finance
Special Issues, Collections and Topics in MDPI journals
Dr. Maria Letizia Guerra

E-Mail Website
Guest Editor
Associate Professor, Department of Statistical Sciences “Paolo Fortunati”, University of Bologna, Bologna, Italy
Interests: financial mathematics; interval and fuzzy mathematics; uncertainty modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The financial markets nowadays are deeply connected with the discipline of mathematics and statistics, which has become increasingly prevalent along with the tremendous growth of modern financial markets worldwide over the past two decades. To understand the underlying mechanisms of financial markets and the complicated behaviour of market participants, a large number of stochastic and computational methods have been proposed by mathematicians and statisticians, and are further applied to address those challenging issues encountered in modern finance. This Special Issue covers the following themes in financial mathematics:

  • Stochastic modelling, including volatility models
  • Stochastic optimal control
  • Asset pricing, involving pricing a range of complex products, including energy and weather derivatives
  • Portfolio selection and asset allocation
  • Financial econometrics and time series
  • High-frequency trading and quantitative investments: data, models and strategies
  • Pension funds and retirement products
  • Insurance and risk theories
  • Financial markets and investor behavior
  • Risk and regulation
  • Financial Technology (FinTech).

Dr. Conghua Wen
Dr. Yi Hong
Dr. Xianming Sun
Prof. Dr. Fei Ma
Dr. Maria Letizia Guerra
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

  • asset pricing
  • quantitative finance and trading
  • portfolio and investment
  • stochastic modelling
  • financial markets
  • insurance and risk management
  • FinTech

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Published Papers (5 papers)

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Research

15 pages, 337 KiB  
Article
Extreme Behavior of Competing Risks with Random Sample Size
by Long Bai, Kaihao Hu, Conghua Wen, Zhongquan Tan and Chengxiu Ling
Axioms 2024, 13(8), 568; https://doi.org/10.3390/axioms13080568 - 21 Aug 2024
Viewed by 521
Abstract
The advances in science and technology have led to vast amounts of complex and heterogeneous data from multiple sources of random sample length. This paper aims to investigate the extreme behavior of competing risks with random sample sizes. Two accelerated mixed types of [...] Read more.
The advances in science and technology have led to vast amounts of complex and heterogeneous data from multiple sources of random sample length. This paper aims to investigate the extreme behavior of competing risks with random sample sizes. Two accelerated mixed types of stable distributions are obtained as the extreme limit laws of random sampling competing risks under linear and power normalizations, respectively. The theoretical findings are well illustrated by typical examples and numerical studies. The developed methodology and models provide new insights into modeling complex data across numerous fields. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics)
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20 pages, 313 KiB  
Article
Strong Comonotonic Additive Systemic Risk Measures
by Heyan Wang, Shuo Gong and Yijun Hu
Axioms 2024, 13(6), 347; https://doi.org/10.3390/axioms13060347 - 23 May 2024
Viewed by 862
Abstract
In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a [...] Read more.
In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a structural decomposition for strong comonotonic additive systemic risk measures. Third, when both the single-firm risk measure and the aggregation function in the structural decomposition are convex, we also provide a dual representation for it. Last, examples are given to illustrate the proposed systemic risk measures. Comparisons with existing systemic risk measures are also provided. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics)
15 pages, 1210 KiB  
Article
Pricing Chinese Convertible Bonds with Learning-Based Monte Carlo Simulation Model
by Jiangshan Zhu, Conghua Wen and Rong Li
Axioms 2024, 13(4), 218; https://doi.org/10.3390/axioms13040218 - 25 Mar 2024
Viewed by 1684
Abstract
In this paper, we explore a novel model for pricing Chinese convertible bonds that seamlessly integrates machine learning techniques with traditional models. The least squares Monte Carlo (LSM) method is effective in handling multiple state variables and complex path dependencies through simple regression [...] Read more.
In this paper, we explore a novel model for pricing Chinese convertible bonds that seamlessly integrates machine learning techniques with traditional models. The least squares Monte Carlo (LSM) method is effective in handling multiple state variables and complex path dependencies through simple regression analysis. In our approach, we incorporate machine learning techniques, specifically support vector regression (SVR) and random forest (RF). By employing Bayesian optimization to fine-tune the random forest, we achieve improved predictive performance. This integration is designed to enhance the precision and predictive capabilities of convertible bond pricing. Through the use of simulated data and real data from the Chinese convertible bond market, the results demonstrate the superiority of our proposed model over the classic LSM, confirming its effectiveness. The development of a pricing model incorporating machine learning techniques proves particularly effective in addressing the complex pricing system of Chinese convertible bonds. Our study contributes to the body of knowledge on convertible bond pricing and further deepens the application of machine learning in the field in an integrated and supportive manner. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics)
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25 pages, 440 KiB  
Article
Modeling Long Memory and Regime Switching with an MRS-FIEGARCH Model: A Simulation Study
by Caixia Zhang and Yanlin Shi
Axioms 2023, 12(5), 446; https://doi.org/10.3390/axioms12050446 - 30 Apr 2023
Cited by 1 | Viewed by 1585
Abstract
Recent research suggests that long memory can be caused by regime switching and is easily confused with it. However, if the causes of confusion were properly controlled, they could be distinguished. Motivated by this idea, our study aims to distinguish between the long [...] Read more.
Recent research suggests that long memory can be caused by regime switching and is easily confused with it. However, if the causes of confusion were properly controlled, they could be distinguished. Motivated by this idea, our study aims to distinguish between the long memory and regime switching of financial volatility. We firstly modeled the long memory and regime switching of volatility using the Fractionally Integrated Exponential GARCH (FIEGARCH) and Markov Regime-Switching EGARCH (MRS-EGARCH) frameworks, respectively, and performed a simulation study on their finite-sample properties when innovations followed a non-normal distribution. Subsequently, we demonstrated the confusion between the FIEGARCH and MRS-EGARCH processes using simulations. A recent study theoretically proved that the time-varying smoothing probability series can induce the presence of significant long memory in the regime-switching process. To control for its effect, the two-stage two-state FIEGARCH and MRS-FIEGARCH frameworks are proposed. The Monte Carlo studies showed that both frameworks can effectively distinguish between the pure FIEGARCH and pure MRS-EGARCH processes. When the MRS-FIEGARCH model was further employed to fit series generated with the MRS-FIEGARCH process, it outperformed the ordinary FIEGARCH model. Finally, an empirical study of NASDAQ index return was conducted to demonstrate that our MRS-FIEGARCH model can provide potentially more reliable long-memory estimates, identify the volatility states and outperform both the FIEGARCH and MRS-EGARCH models. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics)
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17 pages, 384 KiB  
Article
Developments of Efficient Trigonometric Quantile Regression Models for Bounded Response Data
by Suleman Nasiru and Christophe Chesneau
Axioms 2023, 12(4), 350; https://doi.org/10.3390/axioms12040350 - 1 Apr 2023
Viewed by 1474
Abstract
The choice of an appropriate regression model for econometric modeling minimizes information loss and also leads to sound inferences. In this study, we develop four quantile regression models based on trigonometric extensions of the unit generalized half-normal distributions for the modeling of a [...] Read more.
The choice of an appropriate regression model for econometric modeling minimizes information loss and also leads to sound inferences. In this study, we develop four quantile regression models based on trigonometric extensions of the unit generalized half-normal distributions for the modeling of a bounded response variable defined on the unit interval. The desirable shapes of these distributions, such as left-skewed, right-skewed, reversed-J, approximately symmetric, and bathtub shapes, make them competitive models for bounded responses with such traits. The maximum likelihood method is used to estimate the parameters of the regression models, and Monte Carlo simulation results confirm the efficiency of the method. We demonstrate the utility of our models by investigating the relationship between OECD countries’ educational attainment levels, labor market insecurity, and homicide rates. The diagnostics reveal that all our models provide a good fit to the data because the residuals are well behaved. A comparative analysis of the trigonometric quantile regression models with the unit generalized half-normal quantile regression model shows that the trigonometric models are the best. However, the sine unit generalized half-normal (SUGHN) quantile regression model is the best overall. It is observed that labor market insecurity and the homicide rate have significant negative effects on the educational attainment values of the OECD countries. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics)
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