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Mathematical justification of research method of fuzzy set properties of Geske model trajectories and its modifications

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  • Baranov A.O.

  • Muzyko E.I.
  • Pavlov V.N.

Abstract

The purpose of this study is to adapt methods of fuzzy sets to analyze the effectiveness of multistage investment projects. The problem solved by the study is as follows. Some innovative projects are characterized by the lack of profitability in the early stages of implementation and high risk associated with high uncertainty of assessment of expected future cash flows generated by the project. In this situation, the use of standard methods of analysis of economic efficiency of investment projects in high-tech industries, does not provide a comprehensive assessment of the appropriateness of investing, as well as to quantify the accuracy of the dynamics of the projected figures. All this requires the development of theory and methods of analysis of economic efficiency of innovation. Application of real options, as well as the fuzzy sets is, in our view, the direction of improving these methods. The fuzzy random pairs approach is developed in order to study fuzzy set properties of random pointwise set mappings. The articles proposes generalization of the fuzzy random pairs approach for research of stochastic processes. The generalization is initiated by an approach to exploration of uncertainty in research project supported with an RFBR grant no. 15-06-06914, which is based on application of the Geske model modification. Mathematical description of the generalization is carried out for an example of a real venture-backed investment project aimed at organization of methylchloride to ethylene processing. The generalization essence is in the following: 1) time variable t in a random process ( ) ξ t is replaced with a random value u , distributed uniformly within a segment [ ] T ; 0 , which turns the process ( ) ξ t into a bidimensional random value ( ) ( ) ,ξ Vuu = , defined on [ ] R T × ; 0 ; 2) the random value V value is translated into a random pointwise set mapping using the interval translation; 3) in order to translate the random pointwise set mapping into a fuzzy set and to build its membership function a stochastic algorithm is used; 4) for fuzzy set exploration of the resulting pointwise set mapping the fuzzy random pairs approach is used. The solution of the Geske model is a stochastic process defined on a finite segment of time. The article contains main definitions and adaptations of abstract procedures of fuzzy set approach to the real investment project aimed at organization of methyl chloride to ethylene processing. A detailed research of this project attributes with the use of suggested fuzzy set approach lays beyond the frame of the article and should be the subject of an independent applied research.

Suggested Citation

  • Baranov A.O. & Muzyko E.I. & Pavlov V.N., 2016. "Mathematical justification of research method of fuzzy set properties of Geske model trajectories and its modifications," World of economics and management / Vestnik NSU. Series: Social and Economics Sciences, Socionet, vol. 16(2), pages 78-88.
    • Handle: RePEc:nos:wjflnh:2016_2_07e
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
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