BUSINESS INFORM №7-2017

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Section: Economic and Mathematical Modeling
UDC 336.71
Burtnyak I. V., Malytska H. P.
Evaluating the Financial Flows of Bessel Processes by Using Spectral Analysis (p. 120 - 124)
The article solves the two-parameter task of evaluating the intensity of diffuse Bessel processes by the methods of spectral theory. In particular, barriers for cost of options, where the derivative of financial flows turns into zero, have been considered, and a task for the two-barrier option has been solved, which corresponds to Bessel process. A Green’s function has been built for the diffusion Bessel process of the two-barrier option, decomposed according to the first-type system of Bessel functions. The barriers are taken in such a way that the derivative of financial flow in terms of price is turned to zero, i.e. there are the points where flow can acquire extreme values. On the basis of Green’s function, the value of securities has been calculated. It is handier to use similar barriers when monitoring a stock market. The Green’s function for this task, which represents the probability of spreading the option price, is represented through the Fourier series. This provides an opportunity to evaluate the intensity of financial flows in stock markets.
Keywords: spectral theory, barrier option, financial flows, Bessel functions, Green’s function, singular parabolic operator, infinitesimal operator.
Fig.: 1. Formulae: 12. Bibl.: 9.

Burtnyak Ivan V. – Doctor of Sciences (Economics), Associate Professor, Professor, Department of Economic Cybernetics, Vasyl Stefanyk Precarpathian National University (57 Shevchenka Str., Ivano-Frankіvsk, 76018, Ukraine)
Email: [email protected]
Malytska Hanna P. – Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Mathematical and Functional Analysis, Vasyl Stefanyk Precarpathian National University (57 Shevchenka Str., Ivano-Frankіvsk, 76018, Ukraine)

Article is written in English
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Reference to this article:
Burtnyak, Ivan V., and Malytska, Hanna P. (2017) “Evaluating the Financial Flows of Bessel Processes by Using Spectral Analysis.” Business Inform 7:120–124.

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