Research

Research

Research Area

The Centre for Methods of Physics in Economy (Econophysics) belongs to the Faculty of Physics University of Warsaw. This Centre was established in 2006. It’s research staffs is a Group of Interdisciplinary Science of Complex Systems (ISeCS), which makes research and teaching by offering advanced lectures and seminars for graduate and PhD domestic and foreigner students.

Our ISeCS group tightly collaborate with several prominent scientific and academic institutions such as University of Barcelona, ETH-Zürich and Tokyo University.

Challenges defined by economy and sociology very much enrich our scientific interest, for instance, by various theories of statistical time-series (non-linear and non-stationary ones) as well as by advanced numerical simulations and quantitative modelling. They are mainly based on:

Statistical methods including stochastic dynamics, stochastic processes,
phenomenological thermodynamics of equilibrium and non-equilibrium states, an exotic statistical physics (non-Markovian and/or non-Gaussian), theories of phase transitions and catastrophic theories including modelling of black swans and dragon-kings, theories of giant fluctuations and critical phenomena (e.g. self-organized criticality and higher-order phase transitions),

Extreme value theories

Deterministic methods; this category is based, for example, on field theories or theory of deterministic chaos.

The ISeCS group has already great and still developing experience which makes possible to construct comprehensive models describing and forecasting complex economic and social reality full of relations, emotions, conflicts and crashes, based on advanced empirical data analysis and sophisticated theories.

Due to the scientific experience, achievements and sensitivity for real life challenges the ISeCS group cooperate since one year with National Bank of Poland.

In FuturICT the ISeCS would like to find simplicity and some regularity in dynamics of complexity by looking for the latter from complementary points of view. Our project consists of the following complementary subjects:

•From heteroagent micromodels to offer dynamics in the frame of book of orders (PhD student Mateusz Denys).

•Correlations and dependences in offer dynamics on financial markets (PhD student Tomasz Gubiec).

•Modelling of superextreme events and its application to real systems (dr hab. Tomasz Werner).

•Application of catastrophe theory to financial markets (dr Marzena Kozłowska, dr Zbigniew Struzik).

•Multifractality, finite-size scaling and phase transitions on financial markets (dr Andrzej Kasprzak, dr Zbigniew Struzik).

•Unified model of income dynamics (PhD student Maciej Jagielski).

Of course, all given above subjects will based on advanced empirical data analysis and simulations. By solving given above subjects ISeCS will be able to develop the universal dynamics (at least by using an original algorithmic formulation) and propose the possible future scenarios of markets evolution.

Polish Grant awarded within the First Competition of the Committee of Economic Research, organized by the National Bank of Poland, entitled: The preparation of methods for study the extreme and super extreme events' influence on the stochastic dynamics of time series. An application to analysis of some currencies dynamics due to an expectation of the Polish access to euro.

Relevant publications

R. Kutner, A. Pękalski, K. Sznajd-Weron (Eds.): Anomalous Diffusion. From Basics to Applications, Lect. Notes in Phys. Vol. 519, Springer-Verlag, Berlin 1999

R. Kutner: Stock market context of the Lévy walks with varying velocity, Physica A 314 (2002) 201

Z. R. Struzik, A. P. J. M. Siebes, Wavelet Transform Based Multifractal Formalism in Outlier Detection and Localisation for Financial Time Series, Physica A 309 (2002) 388

R. Kutner, F. Świtała: Stochastic Simulation of Time Series within Weierstrass-Mandelbrot Walks, Quant. Finance 3 (2003) 201

M. Kozłowska, R. Kutner: Anomalous transport and diffusion versus extreme value theory, Physica A 357 (2005) 282

K. Kiyono, Z. R. Struzik, Y. Yamamoto, Criticality and PhaseTransition in Stock Price Fluctuations, Phys. Rev. Lett. 96 (2006) 068701

T. Nakamura, K. Kiyono, K. Yoshiuchi, R. Nakahara, Z. R. Struzik, Y. Yamamoto, Universal Scaling Law in Human Behavioural Organization, Phys. Rev. L ett. 99 (2007) 138103

K. Kiyono, Z. R. Struzik, Y. Yamamoto, Estimator of Non-Gaussian Parameter in Multiplicative Log-Normal Mode, Phys. Rev. E 76 (2007)

M. Kozłowska, A. Kasprzak, R. Kutner: Fractional Market Model and its verification on the Warsaw Stock Exchange, Int. J. Modern Phys. C 19 (2008) 453

J. Perelló, J. Masoliver, A. Kasprzak, R. Kutner: Model for interevent times with long tails and multifractality in human communications: An application to financial trading, Phys. Rev. E 78 (2008) 036108.

T. Gubiec, R. Kutner: Backward jump continuous-time random walk: An application to market trading, Phys. Rev. E 82 (2010) 046119

M. Kozłowska, R. Kutner: Singular Dynamics of Various Macroeconomic Sectors, Acta Phys. Pol. A 117 (2010) 630

A. Kasprzak, R. Kutner, J. Perelló, J. Masoliver: Higher-order phase transition on financial markets, Eur. Phys. J. B 76 (2010) 513

M. Jagielski and R. Kutner: Study of Housholds' Income in Poland by using the Statistical Physics Approach, Acta Phys. Pol. A 117 (2010) 615

D.B. Saakian, A. Martirosyan, Chin-Kun Hu and Z. R. Stuzik, /Exact probability distribution function for multifractal random walk models of stocks/, EPL 95 (2011) 2007

T. Gubiec, T. Werner, R. Kutner, D. Sornette: Modeling of super-extreme events: An application to the hierarchical Weierstrass-Mandelbrot Continuous-time Random Walk, Eur. Phys. J. ST 205, 27-52 (2012)

Projects