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Mathematics
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Modern Mathematical Models in Investment: Theory and Practice
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Modern Mathematical Models in Investment: Theory and Practice

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 7911

Special Issue Editors

Prof. Dr. Peter Brusov

E-Mail Website
Guest Editor
Department of Mathematics, Financial University under the Government of Russian Federation, 125993 Moscow, Russia
Interests: financial management; corporate finance; investments; taxation; financial mathematics
Prof. Dr. Tatiana Filatova

E-Mail Website
Guest Editor
Department of Financial and Investment Management, Financial University under the Government of Russian Federation, 125993 Moscow, Russia
Interests: financial management; corporate finance; investments; taxation; financial mathematics

Special Issue Information

Dear Colleagues,

Investments play a crucial role in economy and finance. The role of investment is crucial at the current stage. In this respect, the role of the evaluation of the efficiency of investment projects, which allows for the realization of the most effective projects in the context of scarcity and limited investment resources, has increased. 

In spite of the existence of numerous types of investment models (stochastic, statistics, portfolio etc.), editors are persistent that there are just a few of investment models which could be applied in a real economy.

The purpose of this Special Issue is to bring together developers and users of investment models to discuss problems in this area, relating to what extent existing and new investment models are applicable in real investment practice, how accurately and completely they take into account real investment conditions, and what the advantages and disadvantages of existing investment models are. Both basic models, which are built on the basis of first principles, and applied models using numerical, phenomenological, statistical, and other methods will be considered.

One of the key problems in assessing the effectiveness of investment projects (IP) is the assessment of the discount rate, which plays a crucial role in this assessment.

Some traditional problems, such as the impact on the efficiency of investment of debt financing, project duration, taxation, the value of equity and debt, net operating income, profitability of investments, cost of equity, and debt, will be studied.

Prof. Dr. Peter Brusov
Prof. Dr. Tatiana Filatova
Guest Editors

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Keywords

  • modern mathematical models in investment
  • efficiency of investment and its indicators
  • discount rate
  • debt financing

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Published Papers (4 papers)

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Research

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19 pages, 1258 KiB  
Article
Mathematical Exchange Rates Modeling: Equilibrium and Nonequilibrium Dynamics
by Anton Kuzmin
Mathematics 2022, 10(24), 4672; https://doi.org/10.3390/math10244672 - 9 Dec 2022
Cited by 2 | Viewed by 1911
Abstract
The development of the author’s concept of the International Flows Equilibrium Exchange Rate (IFEER) is the basis for the mathematical exchange rate modeling of two interconnected equal economies. IFEER-concept allows modeling the exchange rate dynamics of relatively medium-term equilibrium and short- and long-term [...] Read more.
The development of the author’s concept of the International Flows Equilibrium Exchange Rate (IFEER) is the basis for the mathematical exchange rate modeling of two interconnected equal economies. IFEER-concept allows modeling the exchange rate dynamics of relatively medium-term equilibrium and short- and long-term disequilibrium. Discrete and integral versions of the concept are the basis for further modeling. New structural models of medium-, short- and long-term dynamics and new final structural dependencies of the exchange rate on the system of fundamental factors are the main results. The models include mathematically formalized export-import and capital flows and international competitive advantages indicators. The modeling allowed the revealing of the structural pricing mechanism of the exchange rate dynamics from new positions. We verify the US dollar to the Russian ruble exchange rate modeling during periods of financial and economic crises in recent Russian history, based on a systematic analysis of the exchange rate policy. Because of the analysis, the fall in export prices of oil and other energy carriers in international markets, the rise in consumer prices within the country, and the fall in aggregate output are the main reasons for the fall of the Russian ruble. The conducted modeling allows for the evaluation of the short-term contribution to the crisis depreciation dynamics. The mathematical tools allow for the development of the decision-making process on the exchange rate regulation. Full article
(This article belongs to the Special Issue Modern Mathematical Models in Investment: Theory and Practice)
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19 pages, 1242 KiB  
Article
Proposed Model of a Dynamic Investment Portfolio with an Adaptive Strategy
by Vera Ivanyuk
Mathematics 2022, 10(23), 4394; https://doi.org/10.3390/math10234394 - 22 Nov 2022
Cited by 2 | Viewed by 1698
Abstract
This article covers a set of models and methods of portfolio investment which help adapt modern economic and mathematical instruments of portfolio investment to the current financial market situation. The main hypotheses serve as a basis for the adaptive dynamic investment portfolio. The [...] Read more.
This article covers a set of models and methods of portfolio investment which help adapt modern economic and mathematical instruments of portfolio investment to the current financial market situation. The main hypotheses serve as a basis for the adaptive dynamic investment portfolio. The experimental analysis shows that the adaptive dynamic investment strategy is more beneficial than classical approaches. The advantage of the adaptive strategy is that it is based on forecast data, whereas classical strategies focus only on historical data. Full article
(This article belongs to the Special Issue Modern Mathematical Models in Investment: Theory and Practice)
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19 pages, 520 KiB  
Article
Estimating Forward-Looking Stock Correlations from Risk Factors
by Wolfgang Schadner and Joshua Traut
Mathematics 2022, 10(10), 1649; https://doi.org/10.3390/math10101649 - 12 May 2022
Viewed by 2150
Abstract
This study provides fully mathematically and economically feasible solutions to estimating implied correlation matrices in equity markets. Factor analysis is combined with option data to receive ex ante beliefs for cross-sectional correlations. Necessary conditions for implied correlation matrices to be realistic, both in [...] Read more.
This study provides fully mathematically and economically feasible solutions to estimating implied correlation matrices in equity markets. Factor analysis is combined with option data to receive ex ante beliefs for cross-sectional correlations. Necessary conditions for implied correlation matrices to be realistic, both in a mathematical and in an economical sense, are developed. An evaluation of existing models reveals that none can comply with the developed conditions consistently. This study overcomes this pitfall and provides two estimation models via exploiting the underlying factor structure of returns. The first solution reformulates the task into a constrained nearest correlation matrix problem. This method can be used either as a stand-alone instrument or as a repair tool to re-establish the feasibility of another model’s estimate. One of these properties is matrix invertibility, which is especially valuable for portfolio optimization tasks. The second solution transforms common risk factors into an implied correlation matrix. The solutions are evaluated upon empirical experiments of S&P 100 and S&P 500 data. They turn out to require modest computational power and comply with the developed constraints. Thus, they provide practitioners with a reliable method to estimate realistic implied correlation matrices. Full article
(This article belongs to the Special Issue Modern Mathematical Models in Investment: Theory and Practice)
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Review

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30 pages, 4302 KiB  
Review
Capital Structure Theory: Past, Present, Future
by Peter Brusov and Tatiana Filatova
Mathematics 2023, 11(3), 616; https://doi.org/10.3390/math11030616 - 26 Jan 2023
Cited by 9 | Viewed by 10288
Abstract
The purpose of this review is to analyze all existing theories of the capital structure (with their advantages and disadvantages) in order to understand all aspects of the problem and make correct management decisions in practice. The role of the capital structure is [...] Read more.
The purpose of this review is to analyze all existing theories of the capital structure (with their advantages and disadvantages) in order to understand all aspects of the problem and make correct management decisions in practice. The role of the capital structure is that the correct determination of the optimal capital structure allows the company’s management to maximize the capitalization of the company and the long-term goal of the function of any company. The review examines the state of the capital structure and capital cost theory from the middle of the last century, when the first quantitative theory was created, to the present. The two main theories, Modigliani–Miller (MM) and Brusov–Filatova–Orekhova (BFO), are discussed and analyzed, as well as their numerous modifications and generalizations. Additionally, discussed is the latest stage in the development of the theory of capital structure, which began a couple of years ago and is associated with the adaptation of the two main theories of capital structure (Brusov–Filatova–Orekhova and Modigliani–Miller) to establish the practice of the function of companies. This generalization takes into account the real conditions of the work of the companies. It was noted that taking into account some effects that are present in economic practice (such as variable income, frequent payments of tax on income, advance payments of tax on income, etc.) brings both theories closer, and even the Modigliani–Miller theory, with all its many limitations, becomes more applicable in economic practice. However, it should be remembered that the Modigliani–Miller theory is only true for perpetual companies, while the BFO theory is valid for companies of any age, and from this point of view, they never coincide. Full article
(This article belongs to the Special Issue Modern Mathematical Models in Investment: Theory and Practice)
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