Dynamic model of investments in research of oligopolia

Publication type Article
Status Published
Occupation: Senior Engineer
Affiliation: Joint-Stock Company «Scientific and Production Association Russian basic information technology
Address: Moscow, Russian Federation
Occupation: Senior Research Scholar
Affiliation: Joint-Stock Company «Scientific and Production Association Russian basic information technology
Address: Russian Federation
Journal nameEkonomika i matematicheskie metody
EditionVolume 56 Issue 2

The authors propose the algorithm for determining the balances on credit line that maximize the current cost of equity capital of an oligopoly company through investment in research. This article is based on the Cournot oligopoly model described in the work by (Vasin, Morozov, 2005). In contrast to the Cournot model, where the static case is investigated, in this article the dynamic extension of the investment model proposed in the work by (Perevozchikov, Lesik, 2014) is studied. This model is a generalization of the classic production problem for a dynamic case and allows to take into account the limitations on limiting leverage, defining an acceptable level of financial sustainability of the company, to formulate sufficient conditions for the company's sustainable growth regime and estimate rates of growth (Perevozchikov, Lesik, Karimov, 2016). The work’s main result is obtaining an explicit expression for the profit of oligopoly in the Cournot model, as a function of the volume of investment in research aimed at reducing the unit cost, from which follows the piecewise differentiability of the criterion in the constructed dynamic expansion of the model. This allows us to apply the projection method of a stochastic gradient with the averaging from the work by (Zavriev, Perevozchikov, 1991) to the obtained problem of discrete optimal control.

Keywordsdynamic investment model, the current cost of equity capital, investment financing, optimal balances on the credit line.
Publication date11.06.2020
Number of characters28296
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1. Brusov P.N., Filatova T.V., Orekhova N.P., Brusov P.P., Brusova A.P. (2011): The cost and structure of capital in the company in the post Modigliani-Miller era // Financial analytics. No.37 (79). P.2-12.

2. Damodaran A. (2010): Investment estimation. Tools and methods of estimation of any assets. Transl. from English. 6th ed. Moscow. Alpina Publishers.

3. Vilensky P.L., Lifshitz V.N., Smolyak S.A. (2004): Estimation of efficiency of investment projects. Theory and practice. Moscow: Delo.

4. Zavriev S.K., Perevozchikov A.G. (1991): A stochastic finite-difference algorithm for minimizing the maximin function // Journal of computational mathematics and mathematical physics. V. 30. No. 4. P. 629 - 633.

5. Makarov V.L., Rubinov F.M. (1973): The Mathematical Theory of Economic Dynamics and equilibrium. Moscow: Nauka.

6. Mesoeconomics (2011): Mesoeconomics of development / ed. by G.B.Kleyner. Moscow: Nauka.

7. Methodology (2003-2005): The methodology and guidance for the estimation of business and / or assets of "UES of Russia" RJSC and subsidiaries and affiliates of "UES of Russia" RJSC. - Deloitte & Touche. - December 2003-March 2005.

8. Minchenko L.I. (1984): Differential properties of the maximum function with related limitations // Journal of computational mathematics and mathematical physics. Vol. 24. No. 2. P. 210-217.

9. Mishchenko A.V., Artemenko O.A. (2012): Models of management of production and financial activities of the enterprise in terms of attracting debt capital // Financial analytics. No. 42 (132).

10. Perevozchikov A.G., Lesik I.A. (2014): Non-stationary model of investment in fixed assets of the enterprise. In collection of papers: "Applied Mathematics and Informatics: Proceedings of the Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University". Ed. by V.I.Dmitriev. Moscow: MAKS Press, No. 46. P.76-88.

11. Perevozchikov A.G., Lesik A.I., Karimov S.D. (2016 b): Conditions for sustainable growth in a dynamic investment model // Audit and financial analysis. No. 5. P. 115 - 116.

12. Perevozchikov A.G., Lesik A.I. (2016). Determination of the optimal production volumes and sales prices in the linear model of multiproduct monopoly // Economics and Mathematical Methods. Vol.52. No. 1. P.140-148.

13. Perevozchikov A.G., Smirnov S.A. (2004): Mixed DDM and CAPM model to estimate the cost of unquoted assets // Economics and Mathematical Methods. Vol.4. No.3. P.118-123.

14. Polyak B.T. (1983): Introduction to optimization. Moscow: Nauka.

15. Fedorov V.V. (1979): Numerical Methods of maximin. Moscow: Nauka.

16. Ashmanov S.A. (1981): Linear Programming. Moscow: Nauka.

17. Sukharev A.G., Timokhov A.V., Fedorov V.V. (1986): Course of optimization techniques. Moscow: Nauka.

18. Perevozchikov A.G., Lesik A.I., Karimov S.D. (2016 a): Differential properties of marginal income function in a linear model of a multi-product monopoly // Audit and financial analysis. No. 1. P. 117 - 121.

19. Perevozchikov A.G., Lesik A.I. (2017): Determination of the optimal balances on a credit line in the dynamic model of investments in company’s fixed assets // Audit and financial analysis. No. 2, P. 94-102.

20. Vasin A.A., Morozov V.V. (2005): Game Theory and Models of Mathematical Economics. Moscow: MAKS Press.

21. Amir R. (1996): Cournot oligopoly and the theory of supermodular games // Games and Economic Behavior. V.15. pp. 132 - 148.

22. Kukushkin N. (1999): A fixed point theorem for decreasing mapping // Economic Letters. V. 46. P. 23 - 26.

23. Novchek W. (1985): On the existence of Cournot equilibrium // Review of Econ. Studies. V. 52. P. 85 - 98.

24. Mikhalevich V.S., Gupal A.M., Norkin V.I. (1987): Non-convex optimization methods. Moscow: Nauka.

25. Vasiliev F.P. (1981): Methods for solving extremal problems. Moscow: Nauka.

26. Perevozchikov A.G. (1991): On approximation of generalized stochastic gradients of random regular functions// Journal of computational mathematics and mathematical physics. V. 30. No. 54. P. 681-688.

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