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Axioms
Special Issues
Financial Mathematics, Stochastic Control, Machine Learning and Related Fields
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Financial Mathematics, Stochastic Control, Machine Learning and Related Fields

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

Deadline for manuscript submissions: closed (30 September 2022) | Viewed by 6105

Special Issue Editors

Dr. Zhou Zhou

E-Mail Website
Guest Editor
School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia
Interests: mathematical finance; optimal stopping; stochastic control and games
Prof. Dr. Xin-Jiang He

E-Mail Website
Guest Editor
School of Economics, Zhejiang University of Technology, Hangzhou 310023, China
Interests: mathematical finance; model calibration; economic modelling; optimization
Dr. Xiang Yu

E-Mail Website
Guest Editor
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
Interests: financial mathematics; stochastic control and optimization; applied probability
Dr. Bin Zou

E-Mail Website
Guest Editor
Department of Mathematics, University of Connecticut, Storrs, CT 06269-1009, USA
Interests: actuarial science; financial mathematics; stochastic control and optimization

Special Issue Information

Dear Colleagues, 

Modern research in financial mathematics, operations research and actuarial science hinges heavily on theoretical tools from probability theory, stochastic control and the theory of PDEs, as well as numerical tools such as the finite difference method, Monte Carlo simulation and machine learning. The purpose of this Special Issue of Axioms is to provide a forum for academics and practitioners to present some current advances in the above-mentioned areas. Topics of this issue include, but are not limited to, the following: 

  • Financial mathematics;
  • Stochastic control and games;
  • Stochastic analysis;
  • Machine learning in finance;
  • Mean field games;
  • Actuarial science;
  • Operations research;
  • Computational finance;
  • Mathematical economics;
  • Risk management;
  • Economic and financial modelling;
  • Probability theory with applications in finance and economics.

Dr. Zhou Zhou
Prof. Dr. Xin-Jiang He
Dr. Xiang Yu
Dr. Bin Zou
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
  • stochastic control
  • machine learning
  • insurance
  • operational research
  • computational finance
  • mathematical economics

Published Papers (4 papers)

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Research

18 pages, 2017 KiB  
Article
A Selective Portfolio Management Algorithm with Off-Policy Reinforcement Learning Using Dirichlet Distribution
by Hyunjun Yang, Hyeonjun Park and Kyungjae Lee
Axioms 2022, 11(12), 664; https://doi.org/10.3390/axioms11120664 - 23 Nov 2022
Viewed by 1387
Abstract
Existing methods in portfolio management deterministically produce an optimal portfolio. However, according to modern portfolio theory, there exists a trade-off between a portfolio’s expected returns and risks. Therefore, the optimal portfolio does not exist definitively, but several exist, and using only one deterministic [...] Read more.
Existing methods in portfolio management deterministically produce an optimal portfolio. However, according to modern portfolio theory, there exists a trade-off between a portfolio’s expected returns and risks. Therefore, the optimal portfolio does not exist definitively, but several exist, and using only one deterministic portfolio is disadvantageous for risk management. We proposed Dirichlet Distribution Trader (DDT), an algorithm that calculates multiple optimal portfolios by taking Dirichlet Distribution as a policy. The DDT algorithm makes several optimal portfolios according to risk levels. In addition, by obtaining the pi value from the distribution and applying importance sampling to off-policy learning, the sample is used efficiently. Furthermore, the architecture of our model is scalable because the feed-forward of information between portfolio stocks occurs independently. This means that even if untrained stocks are added to the portfolio, the optimal weight can be adjusted. We also conducted three experiments. In the scalability experiment, it was shown that the DDT extended model, which is trained with only three stocks, had little difference in performance from the DDT model that learned all the stocks in the portfolio. In an experiment comparing the off-policy algorithm and the on-policy algorithm, it was shown that the off-policy algorithm had good performance regardless of the stock price trend. In an experiment comparing investment results according to risk level, it was shown that a higher return or a better Sharpe ratio could be obtained through risk control. Full article
(This article belongs to the Special Issue Financial Mathematics, Stochastic Control, Machine Learning and Related Fields)
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17 pages, 838 KiB  
Article
Improving the Accuracy of Forecasting Models Using the Modified Model of Single-Valued Neutrosophic Hesitant Fuzzy Time Series
by Kittikun Pantachang, Roengchai Tansuchat and Woraphon Yamaka
Axioms 2022, 11(10), 527; https://doi.org/10.3390/axioms11100527 - 02 Oct 2022
Cited by 1 | Viewed by 1148
Abstract
Proposed in this study is a modified model for a single-valued neutrosophic hesitant fuzzy time series forecasting of the time series data. The research aims at improving the previously presented single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) model by including several degrees of [...] Read more.
Proposed in this study is a modified model for a single-valued neutrosophic hesitant fuzzy time series forecasting of the time series data. The research aims at improving the previously presented single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) model by including several degrees of hesitancy to increase forecasting accuracy. The Gaussian fuzzy number (GFN) and the bell-shaped fuzzy number (BSFN) were used to incorporate the degree of hesitancy. The cosine measure and the single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator were applied to analyze the possibilities and pick the best one based on the neutrosophic value. Two data sets consist of the short and low-frequency time series data of student enrollment and the long and high-frequency data of ten major cryptocurrencies. The empirical result demonstrated that the proposed model provides higher efficiency and accuracy in forecasting the daily closing prices of ten major cryptocurrencies compared to the S-ANFIS, ARIMA, and LSTM methods and also outperforms other FTS methods in predicting the benchmark student enrollment dataset of the University of Alabama in terms of computation time, the Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and the Root Mean Square Error (RMSE). Full article
(This article belongs to the Special Issue Financial Mathematics, Stochastic Control, Machine Learning and Related Fields)
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15 pages, 325 KiB  
Article
Optimal Investment Strategy for DC Pension Plan with Deposit Loan Spread under the CEV Model
by Yang Wang, Xiao Xu and Jizhou Zhang
Axioms 2022, 11(8), 382; https://doi.org/10.3390/axioms11080382 - 04 Aug 2022
Viewed by 1195
Abstract
This paper is devoted to determining an optimal investment strategy for a defined-contribution (DC) pension plan with deposit loan spread under the constant elasticity of variance (CEV) model. As far as we know, few studies in the literature have taken loans into account [...] Read more.
This paper is devoted to determining an optimal investment strategy for a defined-contribution (DC) pension plan with deposit loan spread under the constant elasticity of variance (CEV) model. As far as we know, few studies in the literature have taken loans into account when using the CEV model in financial market contexts. The contribution of this paper is to study the impact of deposit loan spread on DC pension investment strategy. By considering a risk-free asset, a risky asset driven by CEV model, and a loan in the financial market, we first set up the dynamic equation and the asset market model, which are instrumental in achieving the expected utility of ultimate wealth at retirement. Second, the corresponding Hamilton–Jacobi–Bellman (HJB) equation is derived by means of the dynamic programming principle. The explicit expression for the optimal investment strategy is obtained using the Legendre transform method. Finally, different parameters are selected to simulate the explicit solution, and the financial interpretation of the optimal investment strategy is provided. We find that the deposit loan spread has a great impact on the investment strategy of DC pension plans. Full article
(This article belongs to the Special Issue Financial Mathematics, Stochastic Control, Machine Learning and Related Fields)
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11 pages, 245 KiB  
Article
Existence and Stability of Weakly Cooperative Equilibria and Strong Cooperative Equilibria of Multi-Objective Population Games
by Tao Chen, Shih-Sen Chang and Yu Zhang
Axioms 2022, 11(5), 196; https://doi.org/10.3390/axioms11050196 - 22 Apr 2022
Cited by 1 | Viewed by 1441
Abstract
Motivated by the concept of cooperative equilibria with a single objective, we introduce the concepts of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. We give some examples to explain the difference between the cooperative equilibrium point and noncooperative equilibrium [...] Read more.
Motivated by the concept of cooperative equilibria with a single objective, we introduce the concepts of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. We give some examples to explain the difference between the cooperative equilibrium point and noncooperative equilibrium point of multi-objective population games. Under appropriate assumptions, we study the existence and stability of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. Full article
(This article belongs to the Special Issue Financial Mathematics, Stochastic Control, Machine Learning and Related Fields)
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