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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

50200 - Economics and Business

Projekt

<a href="/cs/project/GJ20-25660Y" target="_blank" >GJ20-25660Y: Modelování kreditního a systémového rizika v sektoru neživotního pojištění</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Applied Dynamical Systems

ISSN

1536-0040

e-ISSN

—

Svazek periodika

21

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

2314-2337

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85146372621