Catastrophe theory and price dynamics

 
PIIS042473880003325-6-1
DOI10.31857/S042473880003325-6
Publication type Article
Status Published
Authors
Affiliation: Siberian State University of Science and Technology named after M.F. Reshetnev
Address: Russian Federation, Krasnoyarsk
Journal nameEkonomika i matematicheskie metody
EditionVolume 54 Issue 4
Pages116-123
Abstract

The paper is about finance markets research using non-classical non-linear dynamic methods. Classical time series (including market trends) prediction and analyses methods are based on mathematical statistics. These methods are based on linear and non-linear regression, moving averages and others. Statistical approach assumes that input data honors the normal distribution law. Practice shows that market trends data form normal distribution only on quiet market form and prediction of abrupt shifts is more valuable and important for market analytics. With the evolution of mathematics and social sciences, economists began to apply the differential calculus and its most complicated part — non-linear dynamics — longknown in physics. Starting with Benoit Mandelbrot 1960s works, scientists and analytics widely apply non-linear methods in market terms researches. Mandelbrot started with fractals and power laws; the researches nowadays also apply chaos and catastrophe theory. Catastrophe theory is a big mathematics nonlinear discipline. Catastrophe in terms of mathematics is a discontinuous shift of a system in response to small parameter change. In this paper we apply catastrophe theory to market quotes dynamics. We take market demand and supply as control parameters and trend reverse — as catastrophe. We constructed theoretical model and tested it on real data of property market.

Keywordsnonlinear dynamics, catastrophe theory, assembly-type catastrophe, condition variable, control parameters
Publication date15.01.2019
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1. Arnold V.I. (1990). Catastrophe Theory. Moscow: Nauka (in Russian).

2. Bodie Z., Marcus A.J., Kane A. (2005). Essentials of Investments. Moscow: Williams (in Russian).

3. Gilmor R. (1984). Applicable Catastrophe Theory. Moscow: Mir (in Russian).

4. Mandelbrot B. (2004). Fractals, Hazard and Finance. Moscow, Izhevsk: Reguljarnaja i Haoticheskaja Dinamika (in Russian).

5. Mandelbrot B., Hudson R. (2006). The (Mis)Behavior of Markets. Moscow: Williams (in Russian).

6. Mauboussin M. (2014). More Then You Know. Finding Financial Wisdom. Moscow: Alpina Publisher (in Russian).

7. Mlodinow L. (2011). The Drunkard’s Walk. How Randomness Rules Our Lives. Moscow: Livebook–Gayatri (in Russian).

8. Peters E. (2000). Chaos and Order in the Capital Markets. Moscow: Mir (in Russian).

9. Peters E. (2004). Fractal Market Analyses. Moscow: Internet-trading (in Russian).

10. Stewart I. (1987). Catastrophe Theory and Its Applications. Moscow: Mir (in Russian).

11. Weatherall J. (2013). The Physics of Wall Street. A Brief History of Predicting the Unpredictable. Moscow: Mann, Ivanov i Ferber (in Russian).

12. Zinenko A.V. (2012). R/S Analyses on Stock Market. Business — Informatics, 3 (21), 21–27 (in Russian).

13. Zinenko A.V. (2015a). Pareto Laws on Stock Exchange. Finance and Credit, 38, 11–19 (in Russian).

14. Zinenko A.V. (2015b). MICEX Index Dynamics Analyses With Modern Investment Theory. Krasnoyarsk: Sib SAU (in Russian).

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