Advanced Methods in Mathematical Finance

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 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 250 words) can be sent to the Editorial Office for assessment.

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 semimonthly 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 2600 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.