Options
A 2D piecewise-linear discontinuous map arising in stock market modeling : Two overlapping period-adding bifurcation structures
Gardini, Laura; Radi, Davide; Schmitt, Noemi; u. a. (2023): A 2D piecewise-linear discontinuous map arising in stock market modeling : Two overlapping period-adding bifurcation structures, in: Chaos, solitons & fractals : applications in science and engineering, Amsterdam [u.a.]: Elsevier Science, Jg. 176, Nr. 114143, S. 1–14, doi: 10.1016/j.chaos.2023.114143.
Faculty/Chair:
Author:
Title of the Journal:
Chaos, solitons & fractals : applications in science and engineering
ISSN:
0960-0779
Publisher Information:
Year of publication:
2023
Volume:
176
Issue:
114143
Pages:
Language:
English
Abstract:
We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics of a stock market model. This model is a modification of our previous model associated with a map defined on two partitions. In the present paper, we add more realistic assumptions with respect to the behavior of sentiment traders. Sentiment traders optimistically buy (pessimistically sell) a certain amount of stocks when the stock market is sufficiently rising (falling); otherwise they are inactive. As a result, the action of the price adjustment is represented by a map defined by three different functions, on three different partitions. This leads, in particular, to families of attracting cycles which are new with respect to those associated with a map defined on two partitions. We illustrate how to detect analytically the periodicity regions of these cycles considering the simplest cases of rotation number and obtaining in explicit form the bifurcation boundaries of the corresponding regions. We show that in the parameter space, these regions form two different overlapping period-adding structures that issue from the center bifurcation line. In particular, each point of this line, associated with a rational rotation number, is an issue point for two different periodicity regions related to attracting cycles with the same rotation number but with different symbolic sequences. Since these regions overlap with each other and with the domain of a locally stable fixed point, a characteristic feature of the map is multistability, which we describe by considering the corresponding basins of attraction. Our results contribute to the development of the bifurcation theory for discontinuous maps, as well as to the understanding of the excessively volatile boom-bust nature of stock markets.
GND Keywords: ; ;
Aktienmarkt
Dynamik
Verzweigung <Mathematik>
Keywords: ; ; ; ; ;
2D piecewise-linear discontinuous maps
Border-collision bifurcations
Period-adding bifurcation structure
Coexisting attractors
Center bifurcation
Stock market dynamics
DDC Classification:
RVK Classification:
Peer Reviewed:
Yes:
International Distribution:
Yes:
Type:
Article
Activation date:
November 23, 2023
Versioning
Question on publication
Permalink
https://fis.uni-bamberg.de/handle/uniba/91992