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Symmetry
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Application of symmetry analysis to mathematical biology, engineering, and finance
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Application of symmetry analysis to mathematical biology, engineering, and finance

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 6982

Special Issue Editor

Dr. Nicoleta Bila

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Guest Editor
Fayetteville State University

Special Issue Information

Dear Colleagues,

The current Special Issue is mainly intended at promoting the application of symmetry analysis to nonlinear mathematical models arising in various areas of research, especially to mathematical biology, engineering, and financial mathematics. Researchers at the beginning of their scientific careers are particularly encouraged to submit their manuscripts for publication.

Symmetry reductions are like gold mines. Once they are found, explicit solutions and important properties encapsulated in the nonlinearity of the model are revealed. Symmetry analysis is an alternative method to perturbation, asymptotic, or numerical methods which are often employed to obtain an approximate solution of a model. Over the years, new types of symmetries have been introduced and analyzed in the context of a wide spectrum of applications from mathematical physics, mathematical biology, image processing, engineering, and financial mathematics. For instance, classical Lie symmetries, nonclassical symmetries, potential symmetries, and generalized symmetries have revealed intriguing solutions of various nonlinear differential equations. Presently, new models described by nonlinear differential equations involving arbitrary functions arise more often in applications and spark researchers’ interest. Therefore, for a better understanding of a given mathematical model, finding and exploring new types of symmetry reductions will always be an open field and a challenge for many researchers.

Dr. Nicoleta Bila
Guest Editor

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. Symmetry 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

  • nonlinear models
  • symmetry reductions
  • exact solutions

Published Papers (3 papers)

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Research

17 pages, 2450 KiB  
Article
Forecasting Model for Stock Market Based on Probabilistic Linguistic Logical Relationship and Distance Measurement
by Aiwu Zhao, Junhong Gao and Hongjun Guan
Symmetry 2020, 12(6), 954; https://doi.org/10.3390/sym12060954 - 4 Jun 2020
Cited by 7 | Viewed by 1927
Abstract
The fluctuation of the stock market has a symmetrical characteristic. To improve the performance of self-forecasting, it is crucial to summarize and accurately express internal fluctuation rules from the historical time series dataset. However, due to the influence of external interference factors, these [...] Read more.
The fluctuation of the stock market has a symmetrical characteristic. To improve the performance of self-forecasting, it is crucial to summarize and accurately express internal fluctuation rules from the historical time series dataset. However, due to the influence of external interference factors, these internal rules are difficult to express by traditional mathematical models. In this paper, a novel forecasting model is proposed based on probabilistic linguistic logical relationships generated from historical time series dataset. The proposed model introduces linguistic variables with positive and negative symmetrical judgements to represent the direction of stock market fluctuation. Meanwhile, daily fluctuation trends of a stock market are represented by a probabilistic linguistic term set, which consist of daily status and its recent historical statuses. First, historical time series of a stock market is transformed into a fluctuation time series (FTS) by the first-order difference transformation. Then, a fuzzy linguistic variable is employed to represent each value in the fluctuation time series, according to predefined intervals. Next, left hand sides of fuzzy logical relationships between currents and their corresponding histories can be expressed by probabilistic linguistic term sets and similar ones can be grouped to generate probabilistic linguistic logical relationships. Lastly, based on the probabilistic linguistic term set expression of the current status and the corresponding historical statuses, distance measurement is employed to find the most proper probabilistic linguistic logical relationship for future forecasting. For the convenience of comparing the prediction performance of the model from the perspective of accuracy, this paper takes the closing price dataset of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) as an example. Compared with the prediction results of previous studies, the proposed model has the advantages of stable prediction performance, simple model design, and an easy to understand platform. In order to test the performance of the model for other datasets, we use the prediction of the Shanghai Stock Exchange Composite Index (SHSECI) to prove its universality. Full article
(This article belongs to the Special Issue Application of symmetry analysis to mathematical biology, engineering, and finance)
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15 pages, 334 KiB  
Article
Optimal Investment, Consumption and Leisure with an Option to File for Bankruptcy
by Byung Hwa Lim and Ho-Seok Lee
Symmetry 2020, 12(5), 827; https://doi.org/10.3390/sym12050827 - 18 May 2020
Viewed by 1705
Abstract
This paper investigates the optimal personal bankruptcy decision of a debtor who participates in the labor market. This paper is based on a mathematical finance model that assumes a Black-Scholes financial market and describes a decision problem as an expected discounted utility maximization [...] Read more.
This paper investigates the optimal personal bankruptcy decision of a debtor who participates in the labor market. This paper is based on a mathematical finance model that assumes a Black-Scholes financial market and describes a decision problem as an expected discounted utility maximization problem. Our optimization problem can be cast into a mixed optimal stopping and control problem, and has a symmetry feature with a voluntary retirement decision problem in characterizing the stopping times. To obtain value function and optimal strategies, we use dynamic programming method and transform the relevant nonlinear Bellman equation into a linear equation. Numerical illustrations from our explicit expressions for the optimal strategies reveal how an opportunity to file for bankruptcy affects debtor’s consumption, leisure, and portfolio decisions. Full article
(This article belongs to the Special Issue Application of symmetry analysis to mathematical biology, engineering, and finance)
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19 pages, 1223 KiB  
Article
Analysis of the Spanish IBEX-35 Companies’ Returns Using Extensions of the Fama and French Factor Models
by Francisco Jareño, María de la O González and Laura Munera
Symmetry 2020, 12(2), 295; https://doi.org/10.3390/sym12020295 - 18 Feb 2020
Cited by 5 | Viewed by 2901
Abstract
This paper studies in depth the sensitivity of Spanish companies’ returns to changes in several risk factors between January 2000 and December 2018 using the quantile regression approach. Concretely, this research applies extensions of the Fama and French three- and five-factor models (1993 [...] Read more.
This paper studies in depth the sensitivity of Spanish companies’ returns to changes in several risk factors between January 2000 and December 2018 using the quantile regression approach. Concretely, this research applies extensions of the Fama and French three- and five-factor models (1993 and 2015), according to González and Jareño (2019), adding relevant explanatory factors, such as nominal interest rates, the Carhart (1997) risk factor for momentum and for momentum reversal and the Pastor and Stambaugh (2003) traded liquidity factor. Additionally, for robustness, this paper splits the entire sample period into three sub-sample periods (pre-crisis, crisis and post-crisis) to analyse the results according to the economic cycle. The main conclusions of this paper are fourfold: First, these two models have the greatest explanatory power in the extreme quantiles of the return distribution (0.1 and 0.9) and more specifically in the lowest quantile 0.1. Second, the second model, based on the Fama and French five-factor model, shows the highest explanatory power not only in the full period but also in the three sub-periods. Third, the bank BBVA is the company that shows the highest sensitivity to changes in the explanatory factors in most periods because its adjusted R2 is the highest. Fourth, the stage of the economy with the highest explanatory power is the crisis subperiod. Thus, the final conclusion of this paper is that the second model explains best variations in Spanish companies’ returns in crisis stages and low quantiles. Full article
(This article belongs to the Special Issue Application of symmetry analysis to mathematical biology, engineering, and finance)
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