Università Cattolica del Sacro Cuore


Mercoledì 22 maggio 2024, alle ore 12.00 presso l'Aula 200, Via Necchi 9, si terrà il seminario "A 2D piecewise-linear discontinuous map arising in stock market modeling: Two overlapping period-adding bifurcation structures" tenuto dalla dott.ssa Iryna Sushko, modera il prof. Davide Radi
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 1/n, n>=3, 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.

Giovedì 23 maggio 2024, alle ore 15.00 presso l'Aula G.115 Ruffilli, Largo Gemelli,  si terrà la presentazione del volume "Istanti fatali" - Relatori prof. Umberto Bottazzini, autore e prof. Alfredo Malavolta

Venerdì 24 maggio 2024, alle ore 15.00 presso l'Aula G.018 San Tomaso, Largo Gemelli, si terrà il seminario "L'attuario nell'Internal Audit", Relatori vari