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1
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Ab Initio Analysis of All Income Society Classes in the European Union

100%
Jagielski M., Kutner R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
538-541
EN
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.
2
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Trust in Foreseeing Neighbours - A Novel Threshold Model of Financial Market

100%
Lipski J., Kutner R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
584-588
EN
The three-state agent-based 2D model of financial markets in the version proposed by Giulia Iori in 2002 has been herein extended. We have introduced the increase of herding behaviour by modelling the altering trust of an agent in his nearest neighbours. The trust increases if the neighbour has foreseen the price change correctly and the trust decreases in the opposite case. Our version only slightly increases the number of parameters present in the Iori model. This version well reproduces the main stylized facts observed on financial markets. That is, it reproduces log-returns clustering, fat-tail log-returns distribution and power-law decay in time of the volatility autocorrelation function.
3
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Study of Households' Income in Poland by Using the Statistical Physics Approach

100%
Jagielski M., Kutner R.
Acta Physica Polonica A
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2010
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vol. 117
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issue 4
615-618
EN
At the end of 19th century Vilfredo Pareto, as the first tried by using power-laws to describe wealth and income distributions in society. We applied early works of Pareto as well as Gibrat (i.e. laws of Pareto and rules of proportionate growth, respectively). Furthermore, we used recent and advanced models: the Generalised Lotka-Volterra model and collision models. By using empirical data for annual income of Polish households, e.g. for years 2003 and 2006, the comparison with these theoretical models was successfully made. The surprisingly good agreements with Pareto distribution were obtained, where Pareto exponents near the cubic law were found for middle class. For the low class very good agreement with prediction of the cumulative log-normal distribution was gained. Hence, it was possible to establish the border between low and middle society levels. The same was possible for the border between high and middle classes as the ranking for the former follows (to some extent) the Zipf law.
4
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Singular Dynamics of Various Macroeconomic Sectors

100%
Kozłowska M., Kutner R.
Acta Physica Polonica A
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2010
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vol. 117
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issue 4
630-636
EN
In this work we applied our original solution of the literal Rheological Model of Fractional Dynamics of Financial Market, i.e., the time-dependent solution proportional to the Mittag-Leffler function superposed with oscillations, not only to describe the singular dynamics of financial markets but also to study the singular dynamics of various macroeconomic sectors. The approach makes possible to sufficiently estimate (among others) the time of crash as well as its order. Thus we demonstrate, perhaps useful for stock market investors as well as for various macroeconomic agents, the technical analysis of bubble and crash, which is complementary to the famous one supplying power-law superposed with log-periodic oscillations.
5
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Share Price Evolution as Stationary, Dependent Continuous-Time Random Walk

100%
Gubiec T., Kutner R.
Acta Physica Polonica A
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2010
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vol. 117
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issue 4
669-672
EN
Simple model of share price evolution, which is an extension of Kehr-Kutner-Binder one and Montero-Masoliver models, is presented. The market empirical data inspired the assumptions of the model. The model seems to be the reference one for the study of the short-range correlations in financial data as it considers the observed correlation over two successive jumps of the financial ant.
6
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Report on Foundation and Organization of Econophysics Graduate Courses at Faculty of Physics of University of Warsaw and Department of Physics and Astronomy of the Wrocław University

100%
Kutner R., Grech D.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
637-647
EN
Two different, working examples of organization of econophysics graduate courses at the Faculty of Physics, University of Warsaw and the Department of Physics and Astronomy of the Wrocław University are considered. In the first example we have a system where the interdisciplinary, econophysical education begins only after three years study of physics. Within this system the M.Sc. as well as Ph.D. theses in econophysics are conducted only at the Faculty of Physics. In the second example the B.Sc. theses in econophysics are accomplished in the Department of Physics and Astronomy again after three years study but higher degrees can be prepared either in physics in the Institute of Theoretical Physics or in economy in the Institute of Economical Sciences. M.Sc. and Ph.D. theses can also be conducted. For both examples, the graduate students of econophysics are obliged to participate in traditional (typical) economical lectures and trainings which are offered them by economical departments while lectures and trainings (tutorials and/or laboratory classes) in econophysics are offered them by physics departments themselves. Thus Poland is one of a few countries, where so modern interdisciplinary knowledge is systematically offered to students.
7
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Modern Rheology on a Stock Market: Fractional Dynamics of Indices

100%
Kozłowska M., Kutner R.
Acta Physica Polonica A
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2010
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vol. 118
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issue 4
677-687
EN
This paper presents an exactly solvable (by applying the fractional calculus) the rheological model of fractional dynamics of financial market conformed to the principle of no arbitrage present on financial market. The rheological model of fractional dynamics of financial market describes some singular, empirical, speculative daily peaks of stock market indices, which define crashes as a kind of phase transition. In the frame of the model the plastic market hypothesis and financial uncertainty principle were formulated, which proposed possible scenarios of some market crashes. The brief presentation of the model was made in our earlier work (and references therein). The rheological model of fractional dynamics of financial market is a deterministic model and it is complementary to already existing other ones; together with them it offers possibility for thorough and widespread technical analysis of crashes. The constitutive, fractional integral equation of the model is an analogy of the corresponding one, which defines the fractional Zener model of plastic material. The fractional Zener model is the canonical one for modern rheology, polymer physics and biophysics concerning non-Debye relaxation of viscoelastic biopolymers. The useful approximate solution of the constitutive equation of the rheological model of fractional dynamics of financial market consists of two parts: (i) the first one connected with long-term memory present in the system, which is proportional to the generalized exponential function defined by the Mittag-Leffler function and (ii) the second one describing oscillations (e.g. beats or oscillations having two slightly shifted frequences). The shape exponent leading the Mittag-Leffler function, defines here the order of the phase transition between bullish and bearish states of the financial market, in particular, for recent hossa and bessa on some small, middle and large stock markets. It happened that this solution also successfully estimated some long-term price dynamics on the hypothetical market in United States.
8
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Short Comprehensive Report on the Non-Brownian Stochastic Dynamics at Financial and Commodity Markets

81%
Ciepliński T., Dominiczak A., Kutner R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-24-B-27
EN
In this work we empirically verify the generic breaking of the Central Limit Theorem on the financial and commodity markets. We analysed the distributions of log-returns for typical indices and price of gold, for increasing time horizons. We considered Random Coarse Graining Transformation of the Continuous-Time Random Walk model, which can represent the non-Gaussian price dynamics of underlying assets and the corresponding derivatives, e.g., various options or future contracts. We confirmed that empirical data and predictions of the model quite well agree.
9
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Reinterpretation of Sieczka-Hołyst Financial Market Model

81%
Denys M., Gubiec T., Kutner R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
513-517
EN
In this work we essentially reinterpreted the Sieczka-Hołyst 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 Sieczka-Hołyst 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.
10
Content available remote

Preliminary Comparison of Households' Income in Poland with European Union and United States Ones by Using the Statistical Physics Methods

81%
Jagielski M., Kutner R., Pęczkowski M.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-47-B-49
EN
In this work we compared the empirical data of annual income of Polish and European households as well as annual income of individuals in United States (e.g. for years 2006 and 2008) with predictions of the most popular theoretical models. Particularly good agreements with Pareto distribution and prediction of the Yakovenko model were obtained. For the low society class well agreement with prediction of the cumulative exponential distribution was gained. However, it turned out that the cumulative distribution of annual income of Polish households can be described quite well by the Generalised Lotka-Volterra model.
11
Content available remote

Dynamic Structural and Topological Phase Transitions on the Warsaw Stock Exchange: A Phenomenological Approach

81%
Sienkiewicz A., Gubiec T., Kutner R., Struzik Z.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
615-620
EN
We study crash dynamics of the Warsaw Stock Exchange by using minimal spanning tree networks. We identify the transition of the complex network during its evolution from a (hierarchical) power law minimal spanning tree network - representing the stable state of Warsaw Stock Exchange before the recent worldwide financial crash, to a superstar-like (or superhub) minimal spanning tree network of the market decorated by a hierarchy of trees - an unstable, intermediate market state. Subsequently, we observe a transition from this complex tree to the topology of the (hierarchical) power law minimal spanning tree network decorated by several star-like trees or hubs - this structure and topology represent the Warsaw Stock Exchange after the worldwide financial crash, and can be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets.
12
Content available remote

Comparative Analysis of Income Distributions in the European Union and the United States

81%
Jagielski M., Duczmal R., Kutner R.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-75-A-77
EN
We prove that the most rafined approach - our extension of the Yakovenko et al. model - is a universal in the sense that it well describes both household incomes in the European Union and the individual incomes in the United States for all income social classes. This prove was based on our comparative study of various kinds of incomes. The study constitutes a basis for the finding of an impact of the recent world-wide financial crisis on the volatility of various temporary Pareto exponents and on other parameters of the model.
13
Content available remote

Statistical Collapse of Excessive Market Losses

71%
Denys M., Jagielski M., Gubiec T., Kutner R., Stanley H.
Acta Physica Polonica A
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2016
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vol. 129
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issue 5
913-916
EN
We analytically derive superstatistics (or complex statistics) that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) exhibiting transition thresholds. We measure the interevent times between excessive losses (that is, greater than some threshold) and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential. We find that the scaling shape exponent that drives our superstatistics subordinates themselves and a "superscaling" configuration emerges.
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