Mathematical Finance with Applications

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

Deadline for manuscript submissions: closed (30 June 2020) | Viewed by 55450

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Special Issue Editors


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Guest Editor
1. Department of Finance, Fintech & Blockchain Research Center, Big Data Research Center, Asia University, Taichung City 41354, Taiwan
2. Department of Medical Research, China Medical University Hospital, Taichung City 40447, Taiwan
3. Department of Economics and Finance, The Hang Seng University of Hong Kong, Hong Kong, China
Interests: behavioral models; mathematical modeling; econometrics; energy economics; equity analysis; investment theory; risk management; behavioral economics; operational research; decision theory; environmental economics; public health; time series analysis; forecasting
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Guest Editor
1. School of Statistics, Beijing Normal University, Beijing 100875, China
2. Assistant Research Professor, Department of Statistics, Penn State University, State College, PA, USA
Interests: model checking; missing data; high-dimensional data; decision making under uncertainty

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Guest Editor
Department of Management, Economics and Quantitative Methods, University of Bergamo, Bergamo, Italy
Interests: portfolio theory; mathematical finance; risk management; probability and applications; ordering theory

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 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. Journal of Risk and Financial Management 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 1400 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 (13 papers)

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Editorial

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3 pages, 621 KiB  
Editorial
Editorial Statement for Mathematical Finance
by Wing-Keung Wong
J. Risk Financial Manag. 2020, 13(2), 18; https://doi.org/10.3390/jrfm13020018 - 21 Jan 2020
Cited by 1 | Viewed by 1725
Abstract
Mathematics plays a vital role in many areas of finance and provides the theories and tools that have been widely used in all areas of finance. In this editorial, we tell authors the ideas on what types of papers we will accept for [...] Read more.
Mathematics plays a vital role in many areas of finance and provides the theories and tools that have been widely used in all areas of finance. In this editorial, we tell authors the ideas on what types of papers we will accept for publication in the area of mathematical finance. We will discuss some well-cited papers of mathematical finance. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)

Research

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19 pages, 347 KiB  
Article
Optimal Control Strategies for the Premium Policy of an Insurance Firm with Jump Diffusion Assets and Stochastic Interest Rate
by Dalila Guerdouh, Nabil Khelfallah and Josep Vives
J. Risk Financial Manag. 2022, 15(3), 143; https://doi.org/10.3390/jrfm15030143 - 17 Mar 2022
Cited by 1 | Viewed by 1874
Abstract
In this paper, we present a stochastic optimal control model to optimize an insurance firm problem in the case where its cash-balance process is assumed to be described by a stochastic differential equation driven by Teugels martingales. Noticing that the insurance firm is [...] Read more.
In this paper, we present a stochastic optimal control model to optimize an insurance firm problem in the case where its cash-balance process is assumed to be described by a stochastic differential equation driven by Teugels martingales. Noticing that the insurance firm is able to control its cash-balance dynamics by regulating the underlying premium rate, the aim of the policy maker is to select an appropriate premium in order to minimize the total deviation of the state process to some pre-set target level. As a part of stochastic maximum principle approach, a verification theorem is used to fulfill this achievement. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
25 pages, 10150 KiB  
Article
Mathematical Foundations for Balancing the Payment System in the Trade Credit Market
by Tomaž Fleischman and Paolo Dini
J. Risk Financial Manag. 2021, 14(9), 452; https://doi.org/10.3390/jrfm14090452 - 21 Sep 2021
Cited by 2 | Viewed by 4269
Abstract
The increasingly complex economic and financial environment in which we live makes the management of liquidity in payment systems and the economy in general a persistent challenge. New technologies make it possible to address this challenge through alternative solutions that complement and strengthen [...] Read more.
The increasingly complex economic and financial environment in which we live makes the management of liquidity in payment systems and the economy in general a persistent challenge. New technologies make it possible to address this challenge through alternative solutions that complement and strengthen existing payment systems. For example, interbank balancing and clearing methods (such as real-time gross settlement) can also be applied to private payments, complementary currencies, and trade credit clearing to provide better liquidity and risk management. The paper defines the concept of a balanced payment system mathematically and demonstrates the effects of balancing on a few small examples. It then derives the construction of a balanced payment subsystem that can be settled in full and therefore that can be removed in toto to achieve debt reduction and payment gridlock resolution. Using well-known results from graph theory, the main output of the paper is the proof—for the general formulation of a payment system with an arbitrary number of liquidity sources—that the amount of liquidity saved is maximum, along with a detailed discussion of the practical steps that a lending institution can take to provide different levels of service subject to the constraints of available liquidity and its own cap on total overdraft exposure. From an applied mathematics point of view, the original contribution of the paper is two-fold: (1) the introduction of a liquidity node with a store of value function in obligation-clearing; and (2) the demonstration that the case with one or more liquidity sources can be solved with the same mathematical machinery that is used for obligation-clearing without liquidity. The clearing and balancing methods presented are based on the experience of a specific application (Tetris Core Technologies), whose wider adoption in the trade credit market could contribute to the financial stability of the whole economy and a better management of liquidity and risk overall. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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28 pages, 352 KiB  
Article
An Empirical Analysis of the Volatility Spillover Effect between World-Leading and the Asian Stock Markets: Implications for Portfolio Management
by Imran Yousaf, Shoaib Ali and Wing-Keung Wong
J. Risk Financial Manag. 2020, 13(10), 226; https://doi.org/10.3390/jrfm13100226 - 25 Sep 2020
Cited by 9 | Viewed by 3358
Abstract
This study employs the Vector Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (VAR-AGARCH) model to examine both return and volatility spillovers from the USA (developed) and China (Emerging) towards eight emerging Asian stock markets during the full sample period, the US financial crisis, and the Chinese [...] Read more.
This study employs the Vector Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (VAR-AGARCH) model to examine both return and volatility spillovers from the USA (developed) and China (Emerging) towards eight emerging Asian stock markets during the full sample period, the US financial crisis, and the Chinese Stock market crash. We also calculate the optimal weights and hedge ratios for the stock portfolios. Our results reveal that both return and volatility transmissions vary across the pairs of stock markets and the financial crises. More specifically, return spillover was observed from the US and China to the Asian stock markets during the US financial crisis and the Chinese stock market crash, and the volatility was transmitted from the USA to the majority of the Asian stock markets during the Chinese stock market crash. Additionally, volatility was transmitted from China to the majority of the Asian stock markets during the US financial crisis. The weights of American stocks in the Asia-US portfolios were found to be higher during the Chinese stock market crash than in the US financial crisis. For the majority of the Asia-China portfolios, the optimal weights of the Chinese stocks were almost equal during the Chinese stock market crash and the US financial crisis. Regarding hedge ratios, fewer US stocks were required to minimize the risk for Asian stock investors during the US financial crisis. In contrast, fewer Chinese stocks were needed to minimize the risk for Asian stock investors during the Chinese stock market crash. This study provides useful information to institutional investors, portfolio managers, and policymakers regarding optimal asset allocation and risk management. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
19 pages, 1120 KiB  
Article
Comparison of Financial Models for Stock Price Prediction
by Mohammad Rafiqul Islam and Nguyet Nguyen
J. Risk Financial Manag. 2020, 13(8), 181; https://doi.org/10.3390/jrfm13080181 - 14 Aug 2020
Cited by 23 | Viewed by 10784
Abstract
Time series analysis of daily stock data and building predictive models are complicated. This paper presents a comparative study for stock price prediction using three different methods, namely autoregressive integrated moving average, artificial neural network, and stochastic process-geometric Brownian motion. Each of the [...] Read more.
Time series analysis of daily stock data and building predictive models are complicated. This paper presents a comparative study for stock price prediction using three different methods, namely autoregressive integrated moving average, artificial neural network, and stochastic process-geometric Brownian motion. Each of the methods is used to build predictive models using historical stock data collected from Yahoo Finance. Finally, output from each of the models is compared to the actual stock price. Empirical results show that the conventional statistical model and the stochastic model provide better approximation for next-day stock price prediction compared to the neural network model. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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19 pages, 298 KiB  
Article
Return and Volatility Transmission between World-Leading and Latin American Stock Markets: Portfolio Implications
by Imran Yousaf, Shoaib Ali and Wing-Keung Wong
J. Risk Financial Manag. 2020, 13(7), 148; https://doi.org/10.3390/jrfm13070148 - 08 Jul 2020
Cited by 18 | Viewed by 3829
Abstract
This study uses the BEKK-GARCH model to examine the return-and-volatility spillover between the world-leading markets (USA and China) and four emerging Latin American stock markets over the global financial crisis of 2008 and the crash of the Chinese stock market of 2015. Regarding [...] Read more.
This study uses the BEKK-GARCH model to examine the return-and-volatility spillover between the world-leading markets (USA and China) and four emerging Latin American stock markets over the global financial crisis of 2008 and the crash of the Chinese stock market of 2015. Regarding return spillover, our findings reveal a unidirectional return transmission from Mexico to the US stock market during the global financial crisis. During the crash of the Chinese stock market, the return spillover is found to be unidirectional from the US to the Brazil, Chile, Mexico, and Peru stock markets. Moreover, the results indicate a unidirectional return transmission from China to the Brazil, Chile, Mexico, and Peru stock markets during the global financial crisis and the crash of the Chinese stock market. Regarding volatility spillover, the results show the bidirectional volatility transmission between the US and the stock markets of Chile and Mexico during the global financial crisis. During the Chinese crash, the bidirectional volatility transmission is observed between the US and Mexican stock markets. Furthermore, the volatility spillover is unidirectional from China to the Brazil stock market during the global financial crisis. During the Chinese crash, the volatility spillover is bidirectional between the China and Brazil stock markets. Lastly, a portfolio analysis application has been conducted. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
19 pages, 312 KiB  
Article
The Investment Home Bias with Peer Effect
by Haim Levy
J. Risk Financial Manag. 2020, 13(5), 94; https://doi.org/10.3390/jrfm13050094 - 11 May 2020
Cited by 2 | Viewed by 2106
Abstract
Observed international diversification implies an investment home bias (IHB). Can bivariate preferences with a local domestic peer group rationalize the IHB? For example, it is argued that wishing to have a large correlation with the Standard and Poor’s 500 stock index (S&P 500 [...] Read more.
Observed international diversification implies an investment home bias (IHB). Can bivariate preferences with a local domestic peer group rationalize the IHB? For example, it is argued that wishing to have a large correlation with the Standard and Poor’s 500 stock index (S&P 500 stock index) may induce an increase in the domestic investment weight by American investors and, hence, rationalize the IHB. While this argument is valid in the mean-variance framework, employing bivariate first-degree stochastic dominance (BFSD), we prove that this intuition is generally invalid. Counter intuitively, employing “keeping up with the Joneses” (KUJ) preference with actual international data even enhances the IHB phenomenon. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
18 pages, 474 KiB  
Article
Equity Option Pricing with Systematic and Idiosyncratic Volatility and Jump Risks
by Zhe Li
J. Risk Financial Manag. 2020, 13(1), 16; https://doi.org/10.3390/jrfm13010016 - 17 Jan 2020
Cited by 2 | Viewed by 2929
Abstract
Recently, a large number of empirical studies indicated that individual equity options exhibit a strong factor structure. In this paper, the importance of systematic and idiosyncratic volatility and jump risks on individual equity option pricing is analyzed. First, we propose a new factor [...] Read more.
Recently, a large number of empirical studies indicated that individual equity options exhibit a strong factor structure. In this paper, the importance of systematic and idiosyncratic volatility and jump risks on individual equity option pricing is analyzed. First, we propose a new factor structure model for pricing the individual equity options with stochastic volatility and jumps, which takes into account four types of risks, i.e., the systematic diffusion, the idiosyncratic diffusion, the systematic jump, and the idiosyncratic jump. Second, we derive the closed-form solutions for the prices of both the market index and individual equity options by utilizing the Fourier inversion. Finally, empirical studies are carried out to show the superiority of our model based on the S&P 500 index and the stock of Apple Inc. on options. The out-of-sample pricing performance of our proposed model outperforms the other three benchmark models especially for short term and deep out-of-the-money options. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
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22 pages, 1131 KiB  
Article
CVaR Regression Based on the Relation between CVaR and Mixed-Quantile Quadrangles
by Alex Golodnikov, Viktor Kuzmenko and Stan Uryasev
J. Risk Financial Manag. 2019, 12(3), 107; https://doi.org/10.3390/jrfm12030107 - 26 Jun 2019
Cited by 5 | Viewed by 3863
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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27 pages, 1155 KiB  
Article
Determining Distribution for the Quotients of Dependent and Independent Random Variables by Using Copulas
by Sel Ly, Kim-Hung Pho, Sal Ly and Wing-Keung Wong
J. Risk Financial Manag. 2019, 12(1), 42; https://doi.org/10.3390/jrfm12010042 - 12 Mar 2019
Cited by 20 | Viewed by 3606
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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16 pages, 3574 KiB  
Article
Friendship of Stock Market Indices: A Cluster-Based Investigation of Stock Markets
by László Nagy and Mihály Ormos
J. Risk Financial Manag. 2018, 11(4), 88; https://doi.org/10.3390/jrfm11040088 - 13 Dec 2018
Cited by 6 | Viewed by 4890
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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16 pages, 244 KiB  
Brief Report
Capital Structure and Firm Performance in Australian Service Sector Firms: A Panel Data Analysis
by Rafiuddin Ahmed and Rafiqul Bhuyan
J. Risk Financial Manag. 2020, 13(9), 214; https://doi.org/10.3390/jrfm13090214 - 18 Sep 2020
Cited by 28 | Viewed by 6663
Abstract
Using cross-sectional panel data over eleven years (2009–2019), or 1001 firm-year observations, this study examines the relationship between capital structure and firm performance of service sector firms from Australian stock market. Unlike other studies, in this study directional causalities of all performance measures [...] Read more.
Using cross-sectional panel data over eleven years (2009–2019), or 1001 firm-year observations, this study examines the relationship between capital structure and firm performance of service sector firms from Australian stock market. Unlike other studies, in this study directional causalities of all performance measures were used to identify the cause of firm performance. The study finds that long-term debt dominates debt choices of Australian service sector companies. Although the finding is to some extent similar to trends in debt financed operations observed in companies in developed and developing countries, the finding is unexpected because the sectoral and institutional borrowing rules and regulations in Australia are different from those in other parts of the world. Full article
(This article belongs to the Special Issue Mathematical Finance with Applications)
30 pages, 17174 KiB  
Project Report
Examination and Modification of Multi-Factor Model in Explaining Stock Excess Return with Hybrid Approach in Empirical Study of Chinese Stock Market
by Jian Huang and Huazhang Liu
J. Risk Financial Manag. 2019, 12(2), 91; https://doi.org/10.3390/jrfm12020091 - 25 May 2019
Cited by 2 | Viewed by 4476
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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