Modern approach to modeling of efficiency of financial market based on methods of dynamic programming

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Mukachevo state university

Kharkiv national university of economics named after Semen Kuznets

Modern approach to modeling of efficiency of financial market based on methods of dynamic programming

doctor of economic sciences, professor of the department of management, management of economic processes and tourism

doctor of economic sciences, professor of the department of economic cybernetics and system analysis

PhD in economics, associate professor of the department of accounting, taxation and marketing

doctor of economic sciences, professor of the department of accounting, taxation and marketing

Abstract

Note that any process of financial assets' distribution in the financial market is managed, and classic models of financial market efficiency research are not adapted to the managed behavior of any structure within the operation and decision-making processes regarding their expediency (based on prospective efficiency) can be divided into stages. This makes it necessary to turn to dynamic programming models, which are deprived of the disadvantages of classical models. Therefore, the research is oriented toward forming a modern approach to modeling of efficiency of the financial market based on methods of dynamic programming. Within the framework of the study, it is proved that among the processes of financial market efficiency modeling, there is a systematic combination of steps to be taken to study the process of distribution of financial resources between assets and sources for investments. The study concluded that the F k (X) function and its recursive ratio which reflects possible transformations in the efficiency of operations (recursion) with financial assets, achieved from a specific F k (X), were used to construct the financial market model. The attention actualized on the fact that if F k (X) functions are given statistically, their recurrent ratio can be formed according to the procedures of direct and inverse run to the achievement of values corresponding to the principle of Bellman's optimality. In the study of the distribution of funds, it assumed that: Efficiency F k (X) does not depend on investments into other sources of investment; efficiency from each source of investment is calculated in absolute units of measure; the efficiency of the total investment is equal to the sum of results (profit) received from each investment. The prospects of further research are connected with a developed approach to modeling the financial market efficiency based on dynamic programming methods as one of the tools to ensure further reform and development of the financial sector of Ukraine by the leading international practices and implementation of measures, provided by the Association Agreement between Ukraine and the EU and other international obligations of Ukraine.

Анотація

Будь-який процес розподілення фінансових активів на фінансовому ринку є керованим, а класичні моделі дослідження ефективності фінансового ринку не пристосовані до керованої поведінки будь-якої структури у межах якої операції та процеси прийняття рішення щодо їх доцільності (виходячи з перспективної ефективності) можуть бути розбиті на етапи. Це змушує звернутися до моделей динамічного програмування, які позбавлені виділених нами недоліків класичних моделей. Відтак дослідження орієнтоване на формування сучасного підходу до моделювання ефективності фінансового ринку на основі методів динамічного програмування. У межах дослідження доведено, що серед процесів моделювання ефективності фінансового ринку наявна систематизована сукупність кроків, які потрібно здійснити, щоб дослідити процес розподілу фінансових ресурсів між активами та джерелами для вкладень. При цьому у межах дослідження вдалося дійти висновку, що для побудови моделі фінансового ринку застосовується функція розподілу F k (Х) та її рекурентне співвідношення (що відбиває можливі трансформації у результативності операцій (рекурсії) з фінансовими активами, що досягнути від конкретної F k (Х)). Основну увагу актуалізовано на тому факті, що якщо функції F к (Х) задані статистично, то їх рекурентне співвідношення може формуватися за процедурами прямого та зворотного прогону до досягнення значень, що відповідають принципу оптимальності Беллмана. При дослідженні розподілу ресурсів передбачається, що: результативність функції F к (Х) не залежить від вкладень в інші джерела інвестування; результативність кожного вкладення обчислюється в абсолютних одиницях виміру; сумарна результативність вкладень дорівнює сумі результатів (прибутку), одержаних від кожного вкладення. Перспективи подальших досліджень пов'язані із використанням розробленого підходу до моделювання ефективності фінансового ринку на основі методів динамічного програмування як одного з інструментів забезпечення подальшого реформування та розвитку фінансового сектору України відповідно до провідних міжнародних практик й імплементації заходів, передбачених Угодою про асоціацію між Україною та ЄС й іншими міжнародними зобов «язаннями України.

Ключові слова: ефективність; фінансовий ринок; модель; результативність; операції з фінансовими активами; фінансові ресурси.

Abstract

Problem-solving in general form and its connection with important scientific or practical tasks. In previous research, we have proved that the financial market is a complex neural structure within which the knowledge of internal signals and adaptation to operations with financial assets under such signals is carried out (the basis is a change in the direction of the greatest efficiency of operations). At that, the adjustment process realizes through the stages of decision-making, as to the expediency of carrying out one or another transaction with financial assets. In connection with the described specificity, classic models of financial market efficiency research are uninformative. We state that any process of financial assets' distribution in the financial market is managed. Therefore, the classic models of financial market efficiency unconvertible to the managed behavior of any structure within the operation and decision-making processes regarding their expediency can be divided into stages. This makes it necessary to turn to dynamic programming models, which are deprived of the disadvantages of classical models.

Analysis of recent studies and publications. A significant contribution to the formation and development of the provisions on the development of the methodology for modeling the financial market efficiency and the construction of the corresponding models has been made by many domestic and foreign scientists, such as Batorshyn A. [1], Fabozzi F.J., Zarb F.G. [6], Plastun O., Makarenko I. [5], Dmytrusenko K.O. [2], Paranytsia N.V. [4], etc. In the works of these and other authors, the content of the essence of the concept of efficiency of the financial market is considered, its characteristic features are disclosed, approaches to construction of economic - mathematical models and methods of their analysis and forecasting of the interaction of financial market components are proposed. At the same time, namely modeling and research of the processes of financial assets' distribution in the financial market are still formed by classical models of research (among them are the Irvin model, the non - parametric statistics model, the model autoregressive-forging middle model, the model of a forged middle model, the model of autoregressive, etc. [1, p. 102-119]). Thus, the issue of information-formatting of financial market efficiency models remains the subject of the most important tasks on the given subject and is still not solved.

Formulation of the objectives. The purpose of the article is to form a modern approach to modeling of efficiency of the financial market on the basis of methods of dynamic programming.

The basic material of the research. If we consider the efficiency of the financial market due to the effect of operations with financial assets (including money, various securities, debt obligations and the right of debt claims, etc.), the general content of modeling based on dynamic programming methods should be directed on the construction of a scheme of a managed economic process of distribution of financial resources among sources of their potential increase. Sources of the potential increase of financial resources should be detailed by the financial market structures, and the process of distribution of financial resources by operations with financial assets and sources for investments (what are separate issuers, securities, market participants, etc.).

Therefore, within the framework of financial market efficiency modeling processes, there is a systematic combination of steps to be taken to study the managed economic process of financial resource allocation between assets and sources for investment. The financial market model's construction used the distribution function F k (Х) and its recurrent ratio (this reflects possible transformations in the performance of operations (recursive) with financial assets, which can be achieved from the specific F k (Х)). The functions F k (Х) are statistically given. The recurrent ratio of these functions can be formed and investigated according to the procedures of direct and reverse running to the achievement of the values, overcome which redistribution of financial resources is carried out (it stated that such values orient on the optimal Bellman principle). The analysis of the distribution of funds assumes that:

1) the efficiency of F k (X) does not depend on investments into other sources of investment;

2) the efficiency of each input source is calculated in absolute units of measure;

3) the total efficiency of the deposit is equal to the sum of the results (profit) received from each deposit.

In the first stage of financial market efficiency modeling of specifics of the function F k (X) study should be considered.

In the second stage of the financial market, efficiency modeling should be implemented the construction and study of recursion function F k (X) using the procedure of direct or reverse data run.

Modeling the financial market efficiency should be realized using construction and study of recursion F k (X) according to the direct run data procedure on the condition that Bellman's optimality is the fundamental principle. At the same time, as the components of the research, accepted functions which reflect (from the first step to the last one):

- the maximum result obtained from the deposit (x) at stage 1 given value x1 (f1 (x1));

- maximum efficiency obtained from insertion at stages 1-2 given value x2 (f2 (x2));

- maximum efficiency obtained from insertion at stages 1, 2, 3 given value x3 (f2 (x3)) etc.

Under these conditions, the recurrent ratio for the study of possible transformations of the function Fk(X) will be formed according to the algorithm:

Where: kj - maximum efficiency on distribution taken on acceptable projects or objects of investment; x1…n - an investment of funds into financial assets at the distribution stage of financial resources; j - number of recursions Fk(X).

According to the outlined algorithm of formation of the recurrent correlation of research of the financial market efficiency model should be provided by the algorithm: Because

Where: Cj _ we will allow projects of investments into financial assets; kj - maximum efficiency on distribution taken on acceptable projects.

Let us consider the specificity of the research F k (C) and its recursions firm under reverse data run on condition that as constituents of research uses states of financial market or its subsystems identified:

- by the number of financial resources invested, distributed at stages 1, 2, and 3 (or y1);

- by the number of financial resources invested, distributed at stages 2, 3 (or u2);

- by the number of financial resources invested, distributed at stage 3 (or x3).

At the same time, as the components of the research, accepted functions which reflect (from last to first step):

- the maximum result obtained at stage 3 given value y3 (f3 (y3));

- the maximum result obtained at stages 2, 3 given value y2 (f2 (y2);

- the maximum result obtained at stages 1, 2, and 3 given value y2 (f1 (y1).

Under these conditions, the recurrent ratio for the study of possible transformations of functions FK(X) will be formed according to the algorithm:

financial programming market

Where: kj - maximum efficiency on distribution is taken on acceptable projects or objects of investment (if kj, corresponds with inequality cj(kj) < yj); y1…n - an investment of funds into financial assets at the stage of distribution of financial resources; j - number of functions recursions Fk(y).

Depending on the type of procedures applied, conditional optimal benefits (as the best total result of the system functioning according to a certain type of distribution of financial resources) and conditional optimal management should be determined. With their help, a possible model of efficiency of the financial market and its separate components (in particular, currency market, credit market, deposit market, securities market and derivatives market) is formed. For modeling, it is possible to introduce a system of restrictions in investment based on the number of investment objects and the number of options for investing in such objects.

In particular, modeling the efficiency of the financial market by its complexity and using the procedures of direct data processing can be presented transparently on the example of the currency market. Thus, in conditions of martial law the total volume of banking operations on the currency market of Ukraine (without NBU operations) in August amounted to USD from 0,6451 to 1,7301 million in the equivalent, this is 97,6 percent of this volume being options for investing in the currency offered by such banks as: JSC «Alfa-Bank» (1); JSC «PRIVATBANK» (2); JSC «Citibank» (3); JSC «Raiffeisen Bank» (4), JSC «Ukreximbank» (5); JSC «ING Bank Ukraine» (6); JSC «UKRGAZBANK» (7). Under these conditions, the number of investment objects is equal to 7, and the number of options for investment in such objects is equal to 3. The remaining 2,4 percent should be regarded as background noise. Thus, the input data for modeling the effectiveness of the currency market of Ukraine (without NBU operations) for August 2022 are given in Table 1.

Table 1. Input data for modeling of effectiveness of the currency market of Ukraine (without NBU operations) for August 2022, millions/ thousand USD in equivalent