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**Authors : **1. Vyacheslav Aleksandrovich Slavin,
PhD (Physics and Mathematics), Associate Professor of the Chair of Information Systems and Mathematics

*Saint Petersburg State University for Economics (Cheboksary branch), Cheboksary, Russia*

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Issues of the economic risks theory under direct taxation

**Objective: **to calculate and justify the probabilistic characteristics of the economic risks of the company selling goods with profit and suffering from the burden of direct taxation. The economic nature and mechanisms of tax risks are described.

**Methods:** probabilistic-dynamic method, based on a few mathematically formulated principles – probability principle, the principle of measurement, etc. The method allows to find the optimal distributions of the phase variables (components of the decisions vector) of the production system, numerical characteristics of which (mathematical expectation, variance, covariance, etc.) bear the necessary information about the optimal properties of the economic actors’behavior.

**Results:** the basic equation of probabilistic-dynamic method – the Schrodinger-Bellman equation – was integrated;the function of state was found; the normal distribution was obtained of the vector of economic decisions in the phase space of the firm. The phase trajectories and the effective areas of the variables dispersion phase were researched. It is shown that at the intersection of the variation areas of normal distributions, corresponding to two different production conditions, there is a possibility of spontaneous transitions between these states, accompanied by losses of capital assets of the company. The transition probabilities and the expression for average losses of working capital were calculated. It is shown that the inclusion of weak field tax perturbation leads to the modulation of the probability curves and average losses obtained earlier in the work by V.A. Slavin and I.N. Urusova "Market dynamics of production-economic system. 2. Transitions between production conditions. Elements of risks theory" for the company in the absence of taxation. The author outlines the nature of modulation of the main characteristics of tax risks related to the fact that the tax field influences the production system by phase trajectories perturbation described by periodic functions of time, their frequency equal to the frequency of technological cycles of the firm production units. The work states a number of correlations between the indicators of production processes and taxation processes. The effect of progressive taxation on the company is described.

**Scientific novelty:** for the first time, the aricle demonstrates the possibility to theoretically describe the economic risks of the taxation company and to establish the economic nature of their essential characteristics.

**Practical significance:** the obtained results allow to form a complex of practical programs, aimed at the optimization of the company performance indicators for the purpose of reducing the probability its assets of loss under taxation.

**Keywords : **
Firm; Taxation; Probabilistic-dynamic method; Tax perturbation field; Spontaneous transitions; Probability of tax risks; Average loss of working capital; Optimization

**Bibliography : **
1. Mizgulin, D.A. Metodologicheskie podkhody k opredeleniyu soderzhaniya riskov v sfere nalogooblozheniya i nalogovykh riskov (Methodological approaches to determining the content of risks in the sphere of taxation and taxation risks). Izvestiya Sankt-Peterburgskogo universiteta ekonomiki i finansov, 2011, no. 1, pp. 31–35.

2. Jing, A., Brockett, P.L., William, W. Cooper and Linda L. Golden. Enterprise Risk Management through Strategic Allocation of Capital. Journal of Risk and Insurance, 2012, vol. 79, no. 1, pp. 29–56.

3. Koshkina, G.V., Nikolskaya, V.A. Osobennosti postroeniya matematicheskikh modelei dlya analiza riska bankrotstva predpriyatiya: mat-ly XIV Mezhdunar. konf. "Matematika. Komp'yuter. Obrazovanie", 22–27 yanvarya 2007 g. (Features of building mathematical models to analyze the bankruptcy risks: materials of 14th International conference “Mathematics. Computer. Education”, 22–27 January 2007) / MGU, Biol. f-t. Moscow, 2007.

4. Slavin, V.A., Urusova, I.N. Rynochnaya dinamika proizvodstvenno-ekonomicheskoi sistemy. II. Perekhody mezhdu proizvodstvennymi sostoyaniyami. Elementy teorii riskov (Market dynamics of production-economic system. 2. Transitions between production conditions. Elements of risks theory). Aktual′nye problemy ekonomiki i prava, 2012, no. 4, pp. 170–176.

5. Ivanov, A.G., Kukushkin, (Slavin) V.A. O veroyatnostno-dinamicheskom metode v zadachakh mikroekonomiki (On probability-dynamic method in micro-economic problems). Vestnik NNGU, 2010, no. 1, pp. 179–189.

6. Kukushkin, (Slavin) V.A., Medvedeva, E.V. Planovaya dinamika proizvodstvenno-ekonomicheskikh sistem v rentabel′nom rezhime predlozheniya tovara (Planned dynamics of production-economic system in profitable regime of goods supply). Mezhdunarodnyi nauchnyi zhurnal, 2011, no. 4, pp. 43–48.

7. Slavin, V.A. Rynochnaya dinamika proizvodstvenno-ekonomicheskoi sistemy. I. Korrelyatsionnye svoistva nestatsionarnykh proizvodstvennykh sostoyanii (Market dynamics of production-economic system. 1. Correlation features of unstationary production conditions). Vestnik INZhEKONa, 2012, no 2, pp. 13–21.

8. Kukushkin, (Slavin) V.A. Dinamika proizvodstvenno-ekonomicheskoi sistemy v rezhime statsionarnogo proizvodstva (Dynamics of production-economic system in the regime ofstationary production). Vestnik INZhEKONA. Seriya Ekonomika, 2011, is. 5 (48), pp. 209–219.

**Citation : **
Slavin V.A. Issues of the economic risks theory under direct taxation,Actual Problems of Economics and Law, 2015, No. 3, pp. 92–101.

**Type of article : **The scientific article

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Date of receipt of the article : *

29.06.2015

Date of adoption of the print :

01.08.2015

Date of online accommodation :

15.10.2015