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Axioms
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Financial Mathematics and Econophysics
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Financial Mathematics and Econophysics

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

Deadline for manuscript submissions: 1 December 2024 | Viewed by 3916

Special Issue Editors

Dr. Maria P. Beccar-Varela

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Guest Editor
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
Interests: differential equations; stochastic differential equations; wavelet analysis and discriminant analysis applied to finance, health sciences, and earthquake studies
Prof. Dr. Maria C. Mariani

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Guest Editor
Department of Mathematical Sciences, University of Texas at El Paso, 500 University Ave., Bell Hall 124, El Paso, TX 79968-0514, USA
Interests: stochastic processes; nonlinear partial differential equations; mathematical finance; mathematical physics; numerical methods; geophysics
Special Issues, Collections and Topics in MDPI journals
Dr. Osei K. Tweneboah

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Guest Editor
Department of Data Science, Ramapo College of New Jersey, Mahwah, NJ 07430, USA
Interests: stochastic analysis; machine learning and scientific computing with applications to finance, health sciences and geophysics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We envision a collection of papers in financial mathematics and econophysics, including applications to high-frequency data. Over the past two decades, the complexity of international finance has grown enormously with the development of new markets and instruments for transferring risks. This growth in complexity has been accompanied by an expanded role for mathematical models to value derivative securities and to measure their risks.

At the same time, the new discipline econophysics has advanced. This discipline studies the application of mathematical tools that are usually applied to physical models to the study of financial models. The statistical mechanics theory, such as regarding phase transitions and critical phenomena, has been applied by many authors in studying the speculative bubbles preceding a financial crash.

In the interface of mathematics and financial markets, one specific objective is the development of mathematical models to enhance understanding of extreme events in financial markets.  Specific problems in the mathematics of risk management include the analysis of asset–price dynamics in models that capture the possibility of sudden, large changes in prices—i.e., “jumps”; the development and application of tools from mathematical physics to analyze market dynamics leading to a “crash” and the stochastic volatility extension of the Black–Scholes model applied to the problem of stochastic portfolio optimization.

More recently, there has been unprecedented growth in the amount of financial data and high-frequency data collected and analyzed in quantitative finance and other fields, and modeling and understanding the underlying processes, particularly using high-frequency data, to gain insights into financial markets is a topic of great interest. We recall that some recent notable works on the so-called “May 2010 Flash Crash” include contributions from the areas of quantitative finance, financial engineering, econometrics and government regulator theory.

Dr. Maria P. Beccar-Varela
Prof. Dr. Maria C. Mariani
Dr. Osei K. Tweneboah
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 mathematics
  • econophysics
  • quantitative finance
  • machine Learning
  • high-frequency data
  • complex data sets

Published Papers (2 papers)

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Research

15 pages, 2536 KiB  
Article
Classification of Financial Events and Its Effects on Other Financial Data
by Maria C. Mariani, Osei K. Tweneboah, Md Al Masum Bhuiyan, Maria P. Beccar-Varela and Ionut Florescu
Axioms 2023, 12(4), 372; https://doi.org/10.3390/axioms12040372 - 13 Apr 2023
Viewed by 1082
Abstract
This research classifies financial events, i.e., the collapse of the Lehman Brothers (2008) and the flash crash (2010), and their effects on two different stocks corresponding to Citigroup Inc. (2009) and Iamgold Corporation (2011) to verify if the market data of these years [...] Read more.
This research classifies financial events, i.e., the collapse of the Lehman Brothers (2008) and the flash crash (2010), and their effects on two different stocks corresponding to Citigroup Inc. (2009) and Iamgold Corporation (2011) to verify if the market data of these years were affected more by the crashes of 2008 or 2010. Applying the four techniques, dynamic Fourier methodology, wavelet analysis, discriminant analysis, and clustering analysis, the empirical evidence suggests that the Lehman Brothers’ event is predictable since the dynamics of the dataset can be likened to that of a natural earthquake. On the other hand, the flash crash event is associated with unpredictable explosions. In addition, the dynamics of the stocks from Citigroup (2009) and Iamgold Corporation (2011) are similar to that of the Lehman Brothers collapse. Hence, they are predictable. The accurate classification of the two financial events might help mitigate some of the potential effects of the events. In addition, the methodologies used in this study can help identify the strength of crashes and help practitioners and researchers make informed decisions in the financial market. Full article
(This article belongs to the Special Issue Financial Mathematics and Econophysics)
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17 pages, 1720 KiB  
Article
Data Analysis Using a Coupled System of Ornstein–Uhlenbeck Equations Driven by Lévy Processes
by Maria C. Mariani, Peter K. Asante, William Kubin and Osei K. Tweneboah
Axioms 2022, 11(4), 160; https://doi.org/10.3390/axioms11040160 - 01 Apr 2022
Viewed by 2013
Abstract
In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s [...] Read more.
In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s empirical evidence showing that there exist dependencies or correlations between events; thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of equations. The results show that the solution to the stochastic system provides a good fit to the data sets analyzed. In addition by comparing the results obtained when the BDLP is a Γ(a,b) process or an IG(a,b) process, we are able to deduce the best choice out of the two to model our data sets. Full article
(This article belongs to the Special Issue Financial Mathematics and Econophysics)
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