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Nonlinear random dynamical model for the stock market
P. 012009-1–012009-5.
A new model of a stock market as a nonlinear random dynamical system with additive noise in three-dimensional phase space is offered. Implementations of this model in the adiabatic approximation possess all the key signs of fractal market, making the model a reasonable evolutionary model for a stock market. The use of adiabatic approximation allows us to model a stock market as a nonlinear random dynamical system with multiplicative noise with the power-law in one-dimensional phase space. This model shows fractality, long memory and 1/f noise in a stock market.
In book
Vol. 1298. Issue 1. , Institute of Physics Publishing (IOP), 2019.
Shapoval S., Shapoval B., Shnirman M. G., Scientific Reports 2021 Vol. 11 Article 18151
A cellular automaton constructed by Bak, Tang, and Wiesenfeld (BTW) in 1987 to explain the 1/f noise was recognized by the community for the theoretical foundations of self-organized criticality (SOC). Their conceptual work gave rise to various scientific areas in statistical physics, mathematics, and applied fields. The BTW core principles are based on steady slow loading ...
Added: September 28, 2021
Shapiro Dmitriy S., Remizov S., Nagaev K., JETP Letters 2018 P. 1–5
We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin S = 1/2 of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poissonian noise of the full current I at high frequencies. If the interaction only ...
Added: February 7, 2019
Dmitriev A., Kornilov V., Maltseva S. V., Complexity 2018 Vol. 2018 No. Article ID 4732491 P. 1–11
Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity ...
Added: November 24, 2018
Gromov V., Migrina A., Complexity 2017 Vol. 2017 No. Article ID 9212538 P. 1–7
A natural language (represented by texts generated by native speakers) is considered as a complex system, and the type thereof to which natural languages belong is ascertained. Namely, the authors hypothesize that a language is a self-organized critical system and that the texts of a language are “avalanches” flowing down its word cooccurrence graph. The ...
Added: September 27, 2018
Грицевич М. И., Кузнецова Д. В., Турчак Л. И. et al., Doklady Physics 2016 Vol. 61 No. 6 P. 305–308
An approach to the estimation of the initial shape of a meteoroid based on the statistical distributions of masses of its recovered fragments is presented. The fragment distribution function is used to determine the corresponding scaling index of the power law with exponential cutoff. The scaling index is related empirically to the shape parameter of ...
Added: December 29, 2017
Dmitriev A., Dmitriev V., Silchev V., WSEAS Transactions on Business and Economics 2017 Vol. 14 No. 33 P. 311–321
This paper proposes a nonlinear dynamical model of stock market. Dynamical variables of the model are the variation of ask and bid price relative to equilibrium values and difference between numbers of market agents in a-state and p-state. A particular market agent being in a-state has maximum amount of valuable information about financial asset and ...
Added: November 24, 2017
Dmitriev A., Silchev V., Dmitriev V. et al., , in: Proceedings of International Work-Conference on Time Series (ITISE 2017)Vol. 2.: Granada: Godel Impresiones Digitales S.L., 2017. Ch. 2 P. 1219–1230.
Added: October 19, 2017
Koldanov P.A., Larushina J.D., , in: Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & StatisticsVol. 197.: Springer, 2017. P. 205–214 .
Current approaches to testing hypotheses on degree distribution of the market graph and of identifying power law in data are discussed, main drawbacks of these approaches are identified and ways to overcome them are provided. Brief summary on methodology used is given and main aspects are highlighted. Discussed methodology is applied to testing hypotheses on ...
Added: May 13, 2017
Katchanov Y. L., SpringerPlus 2015 Vol. 4 No. 1 P. eid 677
The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation ...
Added: November 6, 2015
Casault S., Groen A. J., Linton J. D., Science and Public Policy 2013 Vol. 40 No. 2 P. 219–228
This paper provides an improved model, based on historical data, that describes the returns on assets that result from R&D efforts to assist managers of public and private R&D activities. Such a model may lead to better decision support tools to monetize the value that may be extracted from R&D, which is otherwise often undervalued. ...
Added: October 19, 2015
Casault S., Groen A. J., Linton J. D., New Biotechnology 2014 Vol. 31 No. 2 P. 172–178
This paper presents work toward improving the efficacy of financial models that describe the unique nature of biotechnology firms. We show that using a ‘thick tailed’ power law distribution to describe the behavior of the value of biotechnology R&D used in a Real Options Pricing model is significantly more accurate than the traditionally used Gaussian ...
Added: October 19, 2015
Vernikov A. V., Journal of Corporate Finance Research 2013 No. 3(27) P. 23–36
The paper aims to add to the literature on the connection between corporate governance and company valuation. We refer to the case of the Russian banks to suggest that connection between gpvernance and the stock price cannot be established in a convincing way due to data scarcity. Russia's stock market can supply sufficient statistical material ...
Added: November 16, 2013
Korhonen I., Peresetsky A., / Series DP "BOFIT Discussion Papers". 2013. No. 15.
We use a Kalman filter type model of financial markets to extract a global stochastic trend from the discrete non-synchronous data on daily stock market index returns of different stock exchanges. The model is tested for robustness. In addition, we derive “most important” hours of world financial market and estimate the relative importance of local ...
Added: July 21, 2013