Perception of Fundamental Values and Financial Market Dynamics: Mathematical Insights from a 2D Piecewise Linear Map

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F22%3A10251399" target="_blank" >RIV/61989100:27510/22:10251399 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/10.1137/21M1456339" target="_blank" >https://epubs.siam.org/doi/10.1137/21M1456339</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1456339" target="_blank" >10.1137/21M1456339</a>

Result language
angličtina
Original language name
Perception of Fundamental Values and Financial Market Dynamics: Mathematical Insights from a 2D Piecewise Linear Map
Original language description
We develop a simple financial market model in which a market maker adjusts the price with respect to orders placed by chartists and fundamentalists. A novel feature of our model is that fundamentalists optimistically (pessimistically) believe in a relatively high (low) fundamental value when the financial market is increasing (decreasing). As it turns out, the dynamics of our model is driven by a two-dimensional discontinuous piecewise linear map for which we provide an in-depth analytical and numerical investigation. Among other things, we obtain in explicit form the boundaries of the periodicity regions associated with attracting cycles with rotation number 1/n, n geq 3. These boundaries correspond to border collision bifurcations of the related cycles. We show that the periodicity regions are organized in a specific period adding structure, and some of the regions may overlap. Several examples of coexisting cycles and their basins of attraction are also presented. Economically, our results offer a new explanation for the boom-bust behavior of actual financial markets. (C) 2022 Society for Industrial and Applied Mathematics.
Czech name
—
Czech description
—

Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
50200 - Economics and Business

Project
<a href="/en/project/GJ20-25660Y" target="_blank" >GJ20-25660Y: Modeling credit risk and system risk in the non-life insurance sector.</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)