The article proposes conceptual bases of formalization of the investment risk estimation process by means of mathematical and computer modeling on the basis of neural network technologies. The methodological approach to investment risk estimation has been improved. It allows identifying project risk and investment feasibility with using of Hamming neural network accurately and reasonably, reducing the cost of investment making decision and allows self-learning specialized network. The structural hierarchical model of the investment risk estimation process has been improved. It allows decomposing and simplifying the formalization procedure as well as allows simultaneous estimation of the financial ratio of the enterprise and its proposed investment project. The proposed mathematical model was verified and its adequacy was checked by comparing the results obtained on the basis of the application of existing methods and the approach developed by the authors of the article. This revealed the significant advantages of the method proposed in the article. The proposed approach was successfully implemented to estimate the investment risk of 20 domestic enterprises and projects.
Any field of human activity especially the economy and entrepreneurship is burdened by the risk posed by uncertainty, conflicts, variability of goals over time. The problem Copyright © 2020 for this paper by its authors. This volume and its papers are published under the Creative Commons License Attribution 4.0 International (CC BY 4.0). of risk and conflict is inherent in the economy. This is due, in particular, to the fact that the economic process is future-oriented. The external environment in which business organizations of various forms operate becomes qualitatively different: new risk factors appear, the degree of its risk increases. Scientifically based methods of risk estimation and consequently economic feasibility of investment projects (IP), their selection from existing alternatives are becoming increasingly significant. The lack of reliable information base poses a risk to investment decisions. There is always the possibility that a project which was considered attractive will be unprofitable in practice or will not bring the expected profits. This is, in particular, as a result of deviation of the actual values of indicators from those planned in the investment project, inaccurate structure of the investment model, the absence of significant and the presence of insignificant evaluation parameters.
The analysis of the state of real investment processes in Ukraine revealed a number of unresolved practical problems among which the main ones are: the focus of investors on obtaining a one-time fast profit; outflow of national capital; banks' disinterest in long-term crediting; low efficiency of the investment market; insufficient activity of public administration in financing business proposals; imperfection of legislation.
Since the beginning of Volodymyr Zelensky’s presidency a lot of changes have
been made in the legislation of Ukraine, in particular in the field of investments, both
foreign and domestic. On October 3, 2019, the parliament passed a number of laws to
stimulate investment: the law on concessions and the law on the lease of state and
municipal property (new version) [
These problems negatively represent Ukraine in the world investment market and are obstacles to the use of developed investment mechanisms used in countries with post-industrial economies.
Thus, there is an objective need for scientific and theoretical substantiation of the concept and methodological principles of building mathematical methods and models of investment which will take into account the legislative, socio-economic aspect, strategic direction and provide an opportunity to increase investment activity and efficiency results. The generation of modern methodological principles requires the development of a qualitatively new methodological support for the implementation and stimulation of the investment process, i.e. the development of the concept of strategic investment of enterprises in an external environment that is not permanent.
Thus, the development of information tools for investment risk estimation based on modern intellectual technologies is extremely relevant at the present stage of development of Ukraine's economy. 2
At the present stage of market economy development investment activity in Ukraine, despite some recovery in recent years, cannot be considered satisfactory. One of the reasons for this phenomenon is the difficulty of taking risks into account when evaluating investment projects. This causes inaccuracies in investment decisions which, in turn, can not only deprive the investor of the expected return, but also cause him significant losses.
Thus, the problem of investment risk management is one of the most of current interest. The processes of economic development in the crisis under the influence of the coronavirus in the world and in Ukraine have been exacerbated by uncertainty (demand, prices) and competition. To survive in such conditions, business leaders need to introduce new technologies and technical innovations, make bold and unconventional decisions and this increases the degree of economic risk. Therefore, you should learn to predict events, estimate the level and do not go beyond acceptable risk. Business inaction caused by coronavirus quarantine restrictions around the world is also associated with the risk of untapped opportunities.
The risk of both internal and external investors is acceptable and the investment is effective if the enterprise or project in which the investment can be made is profitable. Thus, we first analyze the models that predict the bankruptcy of enterprises that may be potentially investment objects. It allows to identify a potential threat to the timely formation of a system of measures to neutralize the negative trends in the financial situation in the enterprise.
Modern economics has many different techniques and methods for forecasting
financial performance including the estimation of possible bankruptcy [
For example, the paper [
The paper [
Thе article [
The article [
Note that the estimation of crisis symptoms of the enterprise and diagnosing the
possibility of a financial crisis is carried out long before the detection of its obvious
signs [
Beaver’s coefficient [
Altman’s Z-Score model [
Roman Lis’s model [
Taffler’s model [
Fulmer's model [
Springgate’s model, Chesser’s model, Depalian’s model. The models of
Springgate, Cheser and Depalyan are characterized by regression estimates of parameters
that have other values in Ukraine which causes a significant limitation in the
application of these approaches in our country [
An extremely important task of investment projects risk estimation is the
calculation of future cash flows that arise from the sale of manufactured products. This is due
to the fact that only the incoming cash flows are able to ensure the payback of the
investment project. Therefore, they, not profit, are a central factor in valuation. In
other words, the investment decisions risk estimation should be based on the study of
income and expenses in the form of cash flows [
To estimate the effectiveness of investment projects most often are used such
indicators as net present value (NPV), internal rate of return (IRR), profitability index (PI)
and payback period of the project (PP) [
The main disadvantages of the IRR are that it sometimes gives unrealistic income
rates and incorrect answers to the question of which of the two alternative projects
should be chosen, especially if they differ in scale and duration of implementation.
The significant disadvantages of the PP method are that it does not take into account
the cost of invested capital [
It is necessary to distinguish between the financial attractiveness of an individual project and the financial attractiveness of the enterprise that aims to implement this project, if it is an existing enterprise, and compare all the key points of such an enterprise with the key points of the investment project [27, 28, 29].
The complexity of the calculation of indicators and the need to take into account a large number of evaluation parameters requires the creation of an appropriate mathematical model and method of its formalization to estimate the level of investment risk. This approach allows a combination of the most accurate models for assessing the probability of bankruptcy of the investment object and the effectiveness of the investment project [30, 31, 32].
To estimate the investment X * F1 → R risk it is necessary to take into account a large set of input parameters X*, output parameters R and their mapping function. The authors propose to decompose a complex investment problem into a sequence of simpler problems so that the solution of any lower-level problem determines certain parameters in the higher-level problem. The solution of the complex problem of investment risk estimation becomes possible when the solutions of all lower-level subtasks are obtained.
The peculiarity of the investment making decision process is the consistent implementation of the functional F. The task of the investment project risk estimation is to choose an adequate solution R from a set of decisions − possible levels of risk of the IP – Rj, j = 1, n . The authors propose to make a choice based on the classification of investment objects according to investment strategies on the basis of a set of Х evaluation parameters Хi, i = 1, l .
Taking into account all the above factors we offer the following general mathematical model for investment risk estimation: R = {Х*, X, Y, F1, F2, F3},where Х*={x*b} – is the set of primary input parameters, b = 1, k ; X={Xi} – set of evaluation parameters, i = 1, l ; Y={Yj} – generalized set of investment decisions, j = 1, n ; R={Rj} – generalized set of investment decisions j = 1, n ; F1 : Х*→ Х – function of transformation of primary input parameters into evaluation parameters of model; F2 : Х→ Y – generalization function; F3 : Y→ R – function of classification of investment objects according to investment strategies.
To obtain the final result − risk level − R based on the set of primary input parameters X* it is necessary to implement the above functions in the following sequence X * F1 → X F2 →Y F3 → R .
Thus, the authors propose such a structural model of the process of estimation the level of investment risk which is shown in Fig. 1.
The proposed structural model allows classifying IP according to three investment strategies which correspond to the following values of risks Rj: R1 − minimum level of risk: investment is appropriate; R2 − medium level of risk: investment is possible in case of application of risk reduction methods; R3 − high level of risk: investing is impractical.
The proposed structural model allows classifying IP according to three investment strategies which correspond to the following values of risks Rj: R1 − minimum level of risk: investment is appropriate; R2 − medium level of risk: investment is possible in case of application of risk reduction methods; R3 − high level of risk: investing is impractical. Using the method of pairwise comparisons Saati on the basis of questionnaires of employees of credit analysis departments of banking institutions in Vinnytsia was substantiated the limit values of evaluation indicators according to which you can divide the range of values of each of 10 evaluation parameters into three ranges: L − low, M − medium and H − high characteristic level of the indicator (Table 1).
With the development of artificial intelligence systems and computerized information processing tools it becomes possible to productively solve the problem of investment risk estimation. Many experts in this field believe that neural network technologies are aimed at solving classification problems. Thus, the classification of investment entities and investment projects by level of risk is considered by the authors of the article as one of the successful applications of neural networks.
The most productive means of neural technology for investment risk estimation is
the Hamming network. It was developed by Richard Lippman in the middle of 1980’s
[
The choice of the Hamming network among other similar networks is due to its following advantages. It implements the optimal minimum error classifier if the input bit errors are random and independent. A smaller number of neurons is required for the Hamming network to function because the middle layer requires only one neuron per class, instead of a neuron for each input node. Finally, the Hamming network is free of incorrect classifications that may occur, in particular, in the Hopfield network. In general, the Hamming network is both faster and more accurate than the Hopfield network and many other classification networks.
Therefore, to formalize the processes of mapping the set X* to the set R of initial solutions − risk levels Rj the authors of the article propose to use the Hamming neural network. We implement the structural model of the investment risk estimation process built on the basis of the Hamming neural network as shown in Fig. 2.
With the help of expert data and the spectral method of processing expert information 5 reference images of Ep for the neural network were substantiated. They correspond to three levels of investment risk Rj (Table 2). Sets 1 and 2 describe an investment strategy with R1 risk, sets 3 describe a strategy with R2 risk and sets 4 and 5 describe a strategy with R3 risk.
It’s known that the Hamming network works with the numerical values «1» and
«-1» [
The neural network identifies the standard that is closest to the vector fed to its input. The number of this standard Ep allows you to classify the resulting decision to assign the appropriate level of risk R j ( j = 1,3) .
Rj 1 2 3
Therefore, the method of formalization of the proposed mathematical model for estimating the level of investment risk by means of the Hamming neural network is as follows: 1. The input is given the values of the primary indicators X *b(= 1,23) which are used to calculate the evaluation parameters X i (i = 1,10) based on the relevant dependencies. 2. The values of the evaluation parameters Х1…Х10, using the appropriate ranges of values presented in table 1, are described by a specific characteristic level (L − Low, M – Medium, H − High). 3. Each evaluation parameter described by a certain characteristic level is assigned a corresponding binary code. 4. The input vector of the Hamming network have to be formed (coded combination of 20 digits «1» and «-1»). 5. The Hamming neural network identifies the closest to the input vector standard among those described in table 2, the number of which is issued at the network output. In this case, each of the standards corresponds to a certain level of investment risk Rj.
Thus, with the help of the above method it becomes possible to unambiguously classify the object of investment, determine its investment strategy, level of risk and decide on the feasibility of investing. 6
Consider the process of investment risk estimation in the mathematical model proposed by the authors, formalized using the apparatus of the Hamming network, on the example of «Enterprise №1».
For the computer implementation of the proposed Hamming network, the authors of the article have developed a corresponding software product «INVESTOR» based on which the value of the parameters Xi was calculated (as illustrated in Fig. 3) to estimate the level of investment risk of «Enterprise №1».
Based on the developed software product «INVESTOR», the values of the parameters Xi, the linguistic terms corresponding to them, as described in table 1, as well as the corresponding Hamming codes given in table 2, were evaluated. We reduce all these data to the table 3.
This input signal (20-digit Hamming code provided in table 3) was applied to the input of the Hamming neural network which on the basis of the compiled software product identified the nearest input vector standard (among those described in table 2), the number of which was obtained at the output. spond to a high level of risk − R3, therefore investing in such an object is impractical; standard №3 corresponds to R2 − the average level of risk, investment is possible in the case of risk reduction methods; the numbers of standards №4, №5 correspond to R1 − the minimum level of risk which indicates the feasibility of investing in such an object. The conceptual approach proposed by the authors has significant advantages over existing alternative methods: (1) accuracy of estimation; (2) taking into account a wide range of different evaluation parameters; (3) speed; (4) the ability of self-learning.
Using the proposed mathematical model of investment risk estimation (formalized using the Hamming network) allows to eliminate errors in evaluating the investment project, take into account a wide variety of different primary indicators, investor requirements for profitability and payback period project, conduct a simultaneous assessment of bankruptcy, reduce the time to make a final decision on the feasibility of investing.
The main scientific result of the study is the development of conceptual foundations for the formalization of the process of estimation the investment risk level by means of mathematical and computer modeling based on neural network technologies.
The methodological approach to investment risk estimation has been improved which, unlike existing approaches, allows using Hamming neural network to accurately and reasonably identify project risk and assess the feasibility of investing, reduce the cost of such process and allows self-learning specialized network.
The structural hierarchical model of the investment risk estimation process has been improved which carries out its decompositional division and simplifies the formalization on the basis of the mathematical apparatus of the Hamming neural network. It also allows to simultaneously assessing the financial ratio of the entity and its proposed investment project. 27. Vassilenko, V., Valtchev, S., Pamies-Teixeira, J., Pavlov, S.: Energy harvesting: an interesting topic for education programs in engineering specialities. Internet, Education, Science (IES-2016), 149-156 (2016). 28. Krak, Y., Barmak, A., Bagriy, R., Stelya, I.: Text entry system for alternative speech communications. Journal of Automation and Information Sciences, Vol. 49, 1:65–75 (2017). 29. Serkova, V., Pavlov, S., Romanava, V., Monastyrskiy, Yu., Ziepko, S., Kuzminova, N., Wójcik, W., Dzierżak, R., Kalizhanova, A., Kashaganova, G.: Medical expert system for assessment of coronary heart disease destabilization based on the analysis of the level of soluble vascular adhesion molecules. Proc. SPIE 10445, Photonics Applications in Astronomy, Communications, Industry and High Energy Physics Experiments (2017). DOI: 10.1117/12.2280984. 30. Kryvonos, Iu., Krak, Iu., Barmak, O., Bagriy, R.: Predictive text typing system for the Ukrainian language. Cybernetics and systems analysis, Vol. 53, 4:495–502 (2017). DOI: 10.1007/s10559-017-9951-5. 31. Timchenko, L., Pavlov, S., Kokriatskaia, N., Gertsiy, O., Stepaniuk D., Babiuk, N., Kashaganova, G., Harasim, D.: Precision measurement of coordinates of power center of extended laser path images. Proc. SPIE 10808, Photonics Applications in Astronomy, Communications, Industry and High-Energy Physics Experiments (2018). DOI: 10.1117/12.2501628. 32. Azarov, D., Pavlov, S., Chernyak, O., Ivasyuk, I., Wójcik, W., Syzdykpayeva, A.: Principles of fast count in modified Fibonacci numerical system. Proc. SPIE 10808, Photonics Applications in Astronomy, Communications, Industry and High-Energy Physics Experiments (2018). DOI: 10.1117/12.2501565. 33. Lurie, I., Podlevsky, A., Savina, N., Voronenko, M., Pashnina, A., Lytvynenko, V.: Inductive technology of the target clusterization of enterprise’s economic indicators of Ukraine. Proceedings of the Second International Workshop on Computer Modeling and Intelligent Systems (CMIS-2019), рр.848-859, Zaporizhzhia (2019).