Special Issue "Mathematical Finance with Applications"

A special issue of Journal of Risk and Financial Management (ISSN 1911-8074). This special issue belongs to the section "Mathematical Finance".

Deadline for manuscript submissions: 30 September 2019.

Special Issue Editors

Guest Editor
Prof. Dr. Wing-Keung Wong

Department of Finance, College of Management, Asia University, Wufeng, Taichung, Taiwan
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Interests: financial economics; econometrics; mathematical finance; mathematical economics; equity analysis; investment theory; risk management; behavioral finance; behavioral economics; operational research; stochastic dominance theory; time series analysis; Bayesian theory and decision theory; environmental research and public health
Guest Editor
Dr. Xu Guo

School of Statistics, Beijing Normal University, Beijing 100875, China
Assistant Research Professor, Department of Statistics, Penn State University, USA
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Interests: Model Checking, Missing Data, High-dimensional Data, Decision Making Under Uncertainty
Guest Editor
Prof. Dr. Sergio Ortobelli Lozza

University of Bergamo, Bergamo, Italy
Website | E-Mail
Interests: portfolio management; quantitative finance; financial mathematics; financial economics

Special Issue Information

Dear Colleagues,

Mathematical finance plays a vital role in many fields within finance and provides the theories and tools that have been widely used in all areas of finance.

Knowledge of mathematics, probability, and statistics is essential to develop finance theories and test their validity through the analysis of empirical, real-world data. For example, mathematics, probability, and statistics could help to develop pricing models for financial assets such as equities, bonds, currencies, and derivative securities. 

This Special Issue on ‘Mathematical Finance with Applications’, edited by Xu Guo, Sergio Ortobelli, and Wing Keung Wong, will be devoted to related advancements in different areas of finance. The Special Issue will also bring together practical, state-of-the-art applications of mathematics, probability, and statistical techniques in finance.

We invite investigators to contribute original research articles that advance the use of mathematics, probability, and statistics in all areas of finance. All submissions must contain original unpublished work not being considered for publication elsewhere.

Topics of interest include, but are not limited to:

  • Asset pricing and factor models
  • Portfolio optimization
  • Derivative valuation techniques
  • Credit risk and credit rating
  • Numerical and statistical approximation of stochastic differential equations with applications in finance
  • Automated trading systems
  • Statistical arbitrage
  • Financial applications of computational intelligent (neural, fuzzy or evolutionary) methods
  • Behavioral finance
  • Estimation and forecasting of financial time series.
  • Econometric and computational models for risk and financial analysis

Prof. Dr. Wing-Keung Wong
Prof. Dr. Sergio Ortobelli Lozza
Dr. Xu Guo
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 papers will be 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. Journal of Risk and Financial Management is an international peer-reviewed open access quarterly 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 1000 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.

Published Papers (4 papers)

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Research

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Open AccessArticle
CVaR Regression Based on the Relation between CVaR and Mixed-Quantile Quadrangles
J. Risk Financial Manag. 2019, 12(3), 107; https://doi.org/10.3390/jrfm12030107
Received: 16 May 2019 / Revised: 19 June 2019 / Accepted: 20 June 2019 / Published: 26 June 2019
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Abstract
A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called CVaR (superquantile) regression. [...] Read more.
A popular risk measure, conditional value-at-risk (CVaR), is called expected shortfall (ES) in financial applications. The research presented involved developing algorithms for the implementation of linear regression for estimating CVaR as a function of some factors. Such regression is called CVaR (superquantile) regression. The main statement of this paper is: CVaR linear regression can be reduced to minimizing the Rockafellar error function with linear programming. The theoretical basis for the analysis is established with the quadrangle theory of risk functions. We derived relationships between elements of CVaR quadrangle and mixed-quantile quadrangle for discrete distributions with equally probable atoms. The deviation in the CVaR quadrangle is an integral. We present two equivalent variants of discretization of this integral, which resulted in two sets of parameters for the mixed-quantile quadrangle. For the first set of parameters, the minimization of error from the CVaR quadrangle is equivalent to the minimization of the Rockafellar error from the mixed-quantile quadrangle. Alternatively, a two-stage procedure based on the decomposition theorem can be used for CVaR linear regression with both sets of parameters. This procedure is valid because the deviation in the mixed-quantile quadrangle (called mixed CVaR deviation) coincides with the deviation in the CVaR quadrangle for both sets of parameters. We illustrated theoretical results with a case study demonstrating the numerical efficiency of the suggested approach. The case study codes, data, and results are posted on the website. The case study was done with the Portfolio Safeguard (PSG) optimization package, which has precoded risk, deviation, and error functions for the considered quadrangles. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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Open AccessArticle
Determining Distribution for the Quotients of Dependent and Independent Random Variables by Using Copulas
J. Risk Financial Manag. 2019, 12(1), 42; https://doi.org/10.3390/jrfm12010042
Received: 21 February 2019 / Revised: 4 March 2019 / Accepted: 8 March 2019 / Published: 12 March 2019
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Abstract
Determining distributions of the functions of random variables is a very important problem with a wide range of applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient [...] Read more.
Determining distributions of the functions of random variables is a very important problem with a wide range of applications in Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and distribution functions for the quotient Y = X 1 X 2 and the ratio of one variable over the sum of two variables Z = X 1 X 1 + X 2 of two dependent or independent random variables X 1 and X 2 by using copulas to capture the structures between X 1 and X 2 . Thereafter, we extend the theory by establishing the density and distribution functions for the quotients Y = X 1 X 2 and Z = X 1 X 1 + X 2 of two dependent normal random variables X 1 and X 2 in the case of Gaussian copulas. We then develop the theory on the median for the ratios of both Y and Z on two normal random variables X 1 and X 2 . Furthermore, we extend the result of median for Z to a larger family of symmetric distributions and symmetric copulas of X 1 and X 2 . Our results are the foundation of any further study that relies on the density and cumulative probability functions of ratios for two dependent or independent random variables. Since the densities and distributions of the ratios of both Y and Z are in terms of integrals and are very complicated, their exact forms cannot be obtained. To circumvent the difficulty, this paper introduces the Monte Carlo algorithm, numerical analysis, and graphical approach to efficiently compute the complicated integrals and study the behaviors of density and distribution. We illustrate our proposed approaches by using a simulation study with ratios of normal random variables on several different copulas, including Gaussian, Student-t, Clayton, Gumbel, Frank, and Joe Copulas. We find that copulas make big impacts from different Copulas on behavior of distributions, especially on median, spread, scale and skewness effects. In addition, we also discuss the behaviors via all copulas above with the same Kendall’s coefficient. The approaches developed in this paper are flexible and have a wide range of applications for both symmetric and non-symmetric distributions and also for both skewed and non-skewed copulas with absolutely continuous random variables that could contain a negative range, for instance, generalized skewed-t distribution and skewed-t Copulas. Thus, our findings are useful for academics, practitioners, and policy makers. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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Open AccessArticle
Friendship of Stock Market Indices: A Cluster-Based Investigation of Stock Markets
J. Risk Financial Manag. 2018, 11(4), 88; https://doi.org/10.3390/jrfm11040088
Received: 3 November 2018 / Revised: 7 December 2018 / Accepted: 11 December 2018 / Published: 13 December 2018
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Abstract
This paper introduces a spectral clustering-based method to show that stock prices contain not only firm but also network-level information. We cluster different stock indices and reconstruct the equity index graph from historical daily closing prices. We show that tail events have a [...] Read more.
This paper introduces a spectral clustering-based method to show that stock prices contain not only firm but also network-level information. We cluster different stock indices and reconstruct the equity index graph from historical daily closing prices. We show that tail events have a minor effect on the equity index structure. Moreover, covariance and Shannon entropy do not provide enough information about the network. However, Gaussian clusters can explain a substantial part of the total variance. In addition, cluster-wise regressions provide significant and stationer results. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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Other

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Open AccessProject Report
Examination and Modification of Multi-Factor Model in Explaining Stock Excess Return with Hybrid Approach in Empirical Study of Chinese Stock Market
J. Risk Financial Manag. 2019, 12(2), 91; https://doi.org/10.3390/jrfm12020091
Received: 28 April 2019 / Revised: 22 May 2019 / Accepted: 22 May 2019 / Published: 25 May 2019
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Abstract
To search significant variables which can illustrate the abnormal return of stock price, this research is generally based on the Fama-French five-factor model to develop a multi-factor model. We evaluated the existing factors in the empirical study of Chinese stock market and examined [...] Read more.
To search significant variables which can illustrate the abnormal return of stock price, this research is generally based on the Fama-French five-factor model to develop a multi-factor model. We evaluated the existing factors in the empirical study of Chinese stock market and examined for new factors to extend the model by OLS and ridge regression model. With data from 2007 to 2018, the regression analysis was conducted on 1097 stocks separately in the market with computer simulation based on Python. Moreover, we conducted research on factor cyclical pattern via chi-square test and developed a corresponding trading strategy with trend analysis. For the results, we found that except market risk premium, each industry corresponds differently to the rest of six risk factors. The factor cyclical pattern can be used to predict the direction of seven risk factors and a simple moving average approach based on the relationships between risk factors and each industry was conducted in back-test which suggested that SMB (size premium), CMA (investment growth premium), CRMHL (momentum premium), and AMLH (asset turnover premium) can gain positive return. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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