arXiv subjects

Ryszard Kutner

Publications and source records attributed to Ryszard Kutner.

At least 19 recordsLinked to original sources

arXiv2021

Critical phenomena in the market of competing firms induced by state interventionism

We achieve two primary goals in this work. First, we propose a flexible algorithm that can simulate various scenarios of state/government intervention. Secondly, we analyze the scenario exhibiting the critical behavior of the market of competing firms, which depends on the degree of government intervention and the activity level of the firms. Thus, we have analyzed the second-order phase transition series, finding the levels of critical intervention and the critical exponent values. As a result, we have observed a sharp increase of fluctuations at a critical intervention level and the local breakdown of the average market technology concerning the frontier technology.

physics.soc-ph↗

arXiv2020

Government intervention modeling in microeconomic company market evolution

Modern technology and innovations are becoming more crucial than ever for the survival of companies in the market. Therefore, it is significant both from theoretical and practical points of view to understand how governments can influence technology growth and innovation diffusion (TGID) processes. We propose a simple but essential extension of Ausloos-Clippe-Pȩkalski and related Cichy numerical models of the TGID in the market. Both models are inspired by the nonlinear non-equilibrium statistical physics. Our extension involves a parameter describing the probability of government intervention in the TGID process in the company market. We show, using Monte Carlo simulations, the effects interventionism can have on the companies' market, depending on the segment of firms that are supported. The high intervention probability can result, paradoxically, in the destabilization of the market development. It lowers the market's technology level in the long-time limit compared to markets with a lower intervention parameter. We found that the intervention in the technologically weak and strong segments of the company market does not substantially influence the market dynamics, compared to the intervention helping the middle-level companies. However, this is still a simple model which can be extended further and made more realistic by including other factors. Namely, the cost and risk of innovation or limited government resources and capabilities to support companies.

q-fin.GN↗

arXiv2020

Towards a Universal Measure of Complexity

Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity based on the Gell-Mann's view of complexity. Our universal measure of complexity bases on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is optimally mixed states consisting of pure states i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom, is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), ability to the analysis of a system critical behavior, and ability to study the dynamic complexity.

cond-mat.stat-mech↗

arXiv2020

The new face of multifractality: Multi-branchedness and the phase transitions in time series of mean inter-event times

Empirical time series of inter-event or waiting times are investigated using a modified Multifractal Detrended Fluctuation Analysis operating on fluctuations of mean detrended dynamics. The core of the extended multifractal analysis is the non-monotonic behavior of the generalized Hurst exponent $h(q)$ -- the fundamental exponent in the study of multifractals. The consequence of this behavior is the non-monotonic behavior of the coarse Hölder exponent $α(q)$ leading to multi-branchedness of the spectrum of dimensions. The Legendre-Fenchel transform is used instead of the routinely used canonical Legendre (single-branched) contact transform. Thermodynamic consequences of the multi-branched multifractality are revealed. These are directly expressed in the language of phase transitions between thermally stable, metastable, and unstable phases. These phase transitions are of the first and second orders according to Mandelbrot's modified Ehrenfest classification. The discovery of multi-branchedness is tantamount in significance to extending multifractal analysis.

q-fin.ST↗

arXiv2019

Multi-phase long-term autocorrelated diffusion: Stationary continuous-time Weierstrass walk vs. flight

In this paper we are examining diffusion properties of stationary continuous-time Weierstrass walk (CTWW). We are showing it is a multi-phase representation of the Lévy walk. The hierarchical spatial-temporal coupling, combined with coupling between dynamic variables define the CTWW process. The walker moves here with a piecewise constant velocity between trajectory turning points. We have found the diffusion phase diagram of the CTWW consisting not only of anomalous non-Gaussian or non-fBm phases but also Brownian yet non-Gaussian ones. We compare the diffusion phase diagram of the stationary CTWW with the corresponding hierarchical continuous-time Weierstress flight (CTWF). The instantaneous jumps between trajectory turning points preceded by waiting define the CTWF process. It is a hierarchical representation of the Lévy flight. We have found the diffusion phase diagram of the CTWF to be a small part of the corresponding CTWW one.

cond-mat.stat-mech↗

arXiv2016

Continuous-Time Random Walk with multi-step memory: An application to market dynamics

A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale, and justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model turns out to be exactly analytically solvable, which enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus this paper significantly extends the capabilities of the CTRW formalism.

physics.data-an↗

arXiv2016

The Continuous Time Random Walk, still trendy: Fifty-year history, state of art, and outlook

In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different fields of knowledge. A short review of significant achievements and possibilities is given, however, still far from completeness.

cond-mat.stat-mech↗

arXiv2016

Theory of earthquakes interevent times applied to financial markets

We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account how past events influence the occurrence of future events. By analyzing the empirical data for 15 different financial assets, we show that the formalism of the Hawkes process used for earthquakes can successfully model the PDF of interevent times between successive market losses.

q-fin.ST↗

arXiv2016

Income and wealth distribution of the richest Norwegian individuals: An inequality analysis

Using the empirical data from the Norwegian tax office, we analyse the wealth and income of the richest individuals in Norway during the period 2010--2013. We find that both annual income and wealth level of the richest individuals are describable using the Pareto law. We find that the robust mean Pareto exponent over the four-year period to be $\approx 2.3$ for income and $\approx 1.5$ for wealth.

q-fin.GN↗

arXiv2015

Universality of market superstatistics

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde)that exhibit transition thresholds. We measure the interevent times between excessive losses and excessive profits, and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a weighted sum of two components, (i) a powerlaw corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a powerlaw damped by the upper incomplete gamma function, which tends toward the power-law only during short interevent times. We find that the scaling shape exponents that drive both components subordinate themselves and a "superscaling" configuration emerges. We use superstatistics to describe the hierarchical activity when component (i) reproduces the negative feedback and component (ii) reproduces the stylized fact of volatility clustering. Our results indicate that there is a functional (but not literal) balance between excessive profits and excessive losses that can be described using the same body of superstatistics, but different calibration values and driving parameters.

q-fin.ST↗

arXiv2014

Income Distribution in the European Union Versus in the United States

We prove that the refined approach -- our extension of the Yakovenko et al. formalism -- is universal in the sense that it describes well both household incomes in the European Union and the individual incomes in the United States for social classes of any income. This formalism allowed the study of the impact of the recent world-wide financial crisis on the annual incomes of different social classes. Hence, we indicate the existence of a possible precursor of a market crisis. Besides, we find the most painful impact of the crisis on incomes of all social classes.

q-fin.GN↗

arXiv2014

Universality of Tsallis q-exponential of interoccurrence times within the microscopic model of cunning agents

We proposed the agent-based model of financial markets where agents (or traders) are represented by three-state spins located on the plane lattice or social network. The spin variable represents only the individual opinion (advice) that each trader gives to his nearest neighbors. In the model the agents can be considered as cunning. For instance, although agent having currently a maximal value of the spin advises his nearest neighbors to buy some stocks he, perfidiously, will sell some stocks in the next Monte Carlo step or will occupy a neutral position. In general, the trader has three possibilities: he can buy some stocks if his opinion change within a single time step is positive, sell some stocks if this change is negative, or remain inactive if his opinion is unchanged. The predictions of our model, found by simulations, well agree with the empirical universal distribution of interoccurrence times between daily losses below negative thresholds following the Tsallis q-exponential.

q-fin.ST↗

arXiv2013

Agent-Based Stock Market Model with Endogenous Agents' Impact

The three-state agent-based 2D model of financial markets as proposed by Giulia Iori has been extended by introducing increasing trust in the correctly predicting agents, a more realistic consultation procedure as well as a formal validation mechanism. This paper shows that such a model correctly reproduces the three fundamental stylised facts: fat-tail log returns, power-law volatility autocorrelation decay in time and volatility clustering.

q-fin.TR↗

arXiv2013

Modelling of the European Union income distribution by extended Yakovenko formula

We found a unified formula for description of the household incomes of all society classes, for instance, for the European Union in years 2005-2010. The formula is more general than well known that of Yakovenko et al. because, it satisfactorily describes not only the household incomes of low- and medium-income society classes but also the household incomes of the high-income society class. As a striking result, we found that the high-income society class almost disappeared in year 2009, in opposite to situation in remaining years, where this class played a significant role.

q-fin.GN↗

arXiv2013

Modelling the income distribution in the European Union: An application for the initial analysis of the recent worldwide financial crisis

By using methods of statistical physics, we focus on the quantitative analysis of the economic income data descending from different databases. To explain our approach, we introduce the necessary theoretical background, the extended Yakovenko et al. (EY) model. This model gives an analytical description of the annual household incomes of all society classes in the European Union (i.e., the low-, medium-, and high-income ones) by a single unified formula based on unified formalism. We show that the EY model is very useful for the analyses of various income datasets, in particular, in the case of a smooth matching of two different datasets. The completed database which we have constructed using this matching emphasises the significance of the high-income society class in the analysis of all household incomes. For instance, the Pareto exponent, which characterises this class, defines the Zipf law having an exponent much lower than the one characterising the medium-income society class. This result makes it possible to clearly distinguish between medium- and high-income society classes. By using our approach, we found that the high-income society class almost disappeared in 2009, which defines this year as the most difficult for the EU. To our surprise, this is a contrast with 2008, considered the first year of a worldwide financial crisis, when the status of the high-income society class was similar to that of 2010. This, perhaps, emphasises that the crisis in the EU was postponed by about one year in comparison with the United States.

q-fin.GN↗

arXiv2013

Ab initio analysis of all income society classes in the European Union

We found a unified formula for description of the household incomes of all society classes, for instance, of those of the European Union in year 2007. This formula is a stationary solution of the threshold Fokker-Planck equation (derived from the threshold nonlinear Langevin one). The formula is more general than the well known that of Yakovenko et al. because it satisfactorily describes not only household incomes of low- and medium-income society classes but also the household incomes of the high-income society class.

q-fin.GN↗

arXiv2013

Reinterpretation of Sieczka-Hołyst financial market model

In this work we essentially reinterpreted the Sieczka-Hołyst (SH) model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbors to buy some stocks if agents have an opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents' opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the SH model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach.

q-fin.ST↗

arXiv2013

Modeling of income distribution in the European Union with the Fokker-Planck equation

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income)classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker-Planck counterpart, we derived a unified formula for description of income of all society classes, by way of example, of those of the European Union in year 2006 and 2008. Hence, the formula is more general than the well known that of Yakovenko et al. That is, our formula well describes not only two regions but simultaneously the third region in the plot of the complementary cumulative distribution function vs. an annual household income. Furthermore, the known stylised facts concerning this income are well described by our formula. Namely, the formula provides the Boltzmann-Gibbs income distribution function for the low-income society class and the weak Pareto law for the medium-income society class, as expected. Importantly, it predicts (to satisfactory approximation) the Zipf law for the high-income society class. Moreover, the region of medium-income society class is now distinctly reduced because the bottom of high-income society class is distinctly lowered. This reduction made, in fact, the medium-income society class an intermediate-income society class.

q-fin.GN↗