Special Issue "Advanced Methods in Mathematical Finance"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 November 2019

Special Issue Editors

Guest Editor
Prof. Dr. Krzysztof Piasecki

Department of Investment and Real Estate, Poznań University of Economics and Business, al. Niepodległości 10, 61-875 Poznań, Poland
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Interests: operational research; prognostic-decision models; mathematics of fuzzy systems; financial mathematics; financial arithmetic; quantified behavioral finance; econometrics of financial markets
Guest Editor
Dr. Anna Łyczkowska-Hanćkowiak

Institute of Finance, WSB University of Poznań, ul. Powstańców Wielkopolskich 5, 61-895 Poznań, Poland
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Interests: quantified behavioral finance; imprecise in assessing capital markets; operational research; discrete mathematics; graph theory; theory of matroids

Special Issue Information

Dear Colleagues,

Striving for wealth has accompanied people since the dawn of time. Nowadays, it seems that stock exchange investments can be the means to wealth. It is well-known that success in stock exchange investments is not guaranteed only by the investor’s knowledge of the way the stock exchange market functions and how the general economy operates. Along with this knowledge, the other factor that determines success in stock exchange investments is the player’s investment strategy. Models of financial mathematics, classified as applied mathematics, are used to describe the financial market and to create investment strategies. Experience shows that strategies that allow a player to win indefinitely do not exist. Experience indicates that one of the vital factors that guarantees financial success is the use of new, well-created investment methods that are not known to other actors. This causes a specific arms race in financial markets. This race creates demand for new advanced methods of financial mathematics.

These advanced methods can be understood in terms of the modernisation of the classical models of financial mathematics that grew out of the economic grounds of classic logic. The desired direction of development is the extension of models, and the creation of possibilities to include other factors that influence the financial market in these models. In the case of financial mathematics, it is not beneficial to generalise models in a way that does not include new categories of events in financial markets or new economic theories. This is due to the fact that financial mathematics belongs to applied mathematics.

An essential direction for the development of economic theories is the inclusion of descriptions of economic and financial phenomena in terms of multi-valued logic. The consequence of this evolution of financial and economic theories is the creation of advanced methods of financial mathematics and fuzzy financial models. These methods, among other things, reflect the various developmental directions of fuzzy set theories. The main interest of financial mathematics focuses on such fuzzy models, which were created by mathematical deduction. The analysis of the fuzzy financial models created by mathematical induction belongs to the field of operations research.

We can successfully contrast classical economics with behavioural economics. This fact has caused the creation of advanced methods of financial mathematics dedicated to behavioural finance.

The purpose of this Special Issue is to establish a collection of articles that presents the advanced formal methods related to following directions of the development of financial mathematics:

  • classical financial methods in terms of classical logic
  • fuzzy financial models
  • behavioural finance models.

We will also take into consideration justified proposals of other significant directions of the development of financial mathematics. We are motivated by the overriding aim of indicating the connections between mathematical deduction and real finance.

Prof. Dr. Krzysztof Piasecki
Dr. Anna Łyczkowska-Hanćkowiak
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. Mathematics 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 850 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

  • Classical financial mathematics
  • Fuzzy models of financial mathematics
  • Behavioural models of financial mathematics
  • Evaluation of assets
  • Discounting
  • Portfolio analysis
  • Financial risk

Published Papers (3 papers)

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Research

Open AccessArticle
Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas
Mathematics 2019, 7(3), 274; https://doi.org/10.3390/math7030274
Received: 29 January 2019 / Revised: 9 March 2019 / Accepted: 14 March 2019 / Published: 18 March 2019
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Abstract
Multivariate copulas have been widely used to handle risk in the financial market. This paper aimed to adopt two novel multivariate copulas, Vine copulas and Factor copulas, to measure and compare the financial risks of the emerging economy, developed economy, and global economy. [...] Read more.
Multivariate copulas have been widely used to handle risk in the financial market. This paper aimed to adopt two novel multivariate copulas, Vine copulas and Factor copulas, to measure and compare the financial risks of the emerging economy, developed economy, and global economy. In this paper, we used data from three groups (BRICS, which stands for emerging markets, specifically, those of Brazil, Russia, India, China, and South Africa; G7, which refers to developed countries; and G20, which represents the global market), separated into three periods (pre-crisis, crisis, and post-crisis) and weighed Value at Risk (VaR) and Expected Shortfall (ES) (based on their market capitalization) to compare among three copulas, C-Vine, D-Vine, and Factor copulas. Also, real financial data demonstrated that Factor copulas have stronger stability and perform better than the other two copulas in high-dimensional data. Moreover, we showed that BRICS has the highest risk and G20 has the lowest risk of the three groups. Full article
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
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Open AccessFeature PaperArticle
Sharpe’s Ratio for Oriented Fuzzy Discount Factor
Mathematics 2019, 7(3), 272; https://doi.org/10.3390/math7030272
Received: 10 January 2019 / Revised: 1 March 2019 / Accepted: 12 March 2019 / Published: 16 March 2019
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Abstract
The analysis presented in this paper regards the security of a present value given as an ordered fuzzy number. The present value was estimated in an imprecise manner and supplemented by the forecast of its coming changes. A discount factor of such security [...] Read more.
The analysis presented in this paper regards the security of a present value given as an ordered fuzzy number. The present value was estimated in an imprecise manner and supplemented by the forecast of its coming changes. A discount factor of such security is an ordered fuzzy number of the orientation identical to the oriented present value that determines it. All classical methods of portfolio analysis are based on the definition of the return rate. In the case of securities with a fuzzy present value, a discount factor is a better tool for portfolio analysis than the return rate, which implies the chosen methods of management of securities should be revised and transformed to equivalent methods based on a discount factor. This would enable the use of those methods in the case of a financial instrument of the oriented fuzzy present value. This paper presents example results of the realization of such a postulate. The main aim of the paper is to generalize Sharpe’s ratio to a case of investment recommendations management formulated for a security characterized by an oriented discount factor. A five-degree rating scale was used. The whole deliberation is illustrated by broad numerical examples. Full article
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
Open AccessArticle
Evaluation of the Impact of Strategic Offers on the Financial and Strategic Health of the Company—A Soft System Dynamics Approach
Mathematics 2019, 7(2), 208; https://doi.org/10.3390/math7020208
Received: 29 December 2018 / Revised: 14 February 2019 / Accepted: 19 February 2019 / Published: 24 February 2019
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Abstract
When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be based on rationality and the [...] Read more.
When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be based on rationality and the characteristics of the system being modeled. Such an approach implies the use of an appropriate analysis and modeling method. Since the majority of relationships in the model are described using the experts’ tacit knowledge, methods known as “soft” are more suitable than “hard” in those situations. Fuzzy cognitive mappings (FCM) are therefore commonly used as a technique for participatory modeling of the system, where stakeholders can convey their knowledge to the model of the system in question. In this study, we introduce a novel approach: the extended weighted influence nonlinear gauge system (WINGS), which may equally well be applied to the decision problems of this type. Appraisal of high-value and long-term offers in the sector of the telecommunication supplier industry serves as a real-world case study for testing the new method. A comparison with FCM provides a deeper understanding of the similarities and differences of the two approaches. Full article
(This article belongs to the Special Issue Advanced Methods in Mathematical Finance)
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