arXiv subjects

Ryszard Kutner

Publications and source records attributed to Ryszard Kutner.

21 records · Page 2Linked to original sources

arXiv2013

Trust in foreseeing neighbours - a novel threshold model of financial market

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.

q-fin.TR↗

arXiv2010

Super-extreme event's influence on a Weierstrass-Mandelbrot Continuous-Time Random Walk

Two utmost cases of super-extreme event's influence on the velocity autocorrelation function (VAF) were considered. The VAF itself was derived within the hierarchical Weierstrass-Mandelbrot Continuous-Time Random Walk (WM-CTRW) formalism, which is able to cover a broad spectrum of continuous-time random walks. Firstly, we studied a super-extreme event in a form of a sustained drift, whose duration time is much longer than that of any other event. Secondly, we considered a super-extreme event in the form of a shock with the size and velocity much larger than those corresponding to any other event. We found that the appearance of these super-extreme events substantially changes the results determined by extreme events (the so called "black swans") that are endogenous to the WM-CTRW process. For example, changes of the VAF in the latter case are in the form of some instability and distinctly differ from those caused in the former case. In each case these changes are quite different compared to the situation without super-extreme events suggesting the possibility to detect them in natural system if they occur.

physics.data-an↗

arXiv2006

Dynamics of the Warsaw Stock Exchange index as analysed by the nonhomogeneous fractional relaxation equation

We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be described by the Mittag-Leffler function superposed with various types of oscillations. The latter is a solution of our model of index dynamics defined by the nonhomogeneous fractional relaxation equation. This solution is a generalised analog of an exactly solvable model of viscoelastic materials. We found that the Warsaw Stock Exchange can be considered as an intermediate system lying between two complex ones, defined by short and long-time limits of the Mittag-Leffler function; these limits are given by the Kohlraush-Williams-Watts law for the initial times, and the power-law or the Nutting law for asymptotic time. Hence follows the corresponding short- and long-time power-law behaviour (different universality classes) of the time-derivative of the logarithm of WIG which can in fact be viewed as the finger print of a dynamical critical phenomenon.

physics.soc-ph↗