Quantum model for the price dynamics: The problem of smoothness of trajectories
type: Item
instance of: scholarly article
title: Quantum model for the price dynamics: The problem of smoothness of trajectories
zbMATH Open document ID: 1153.91017
author: Olga Choustova
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-07-21T00:00:00Z
review text: A new approach to the modeling of financial market is considered, that is not based on the assumption that investors act rationally and without bias. Instead, information about financial market is described by an information field \(\psi(t,q)\) -- financial wave (this model of quantum mechanics is named Bohmian model). Dynamics is described by the trajectory in the configuration price space and is given by Schrödinger equation on the space of prices or shares. It is shown that even continuous dynamics of the financial wave can produce discontinuous quantum force, so, can induce jumps of prices of shares. Existence theorems are proved for equations with discontinuous classical and quantum forces.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 81-XX
zbMATH DE Number: 5303214
zbMATH Keywords: Quantum-like models
zbMATH Keywords: price dynamics
zbMATH Keywords: smoothness of trajectories
zbMATH Keywords: existence theorems
zbMATH Keywords: discontinuous potentials
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.04.072
OpenAlex ID: W2080209783
cites work: Information dynamics in cognitive, psychological, social and anomalous phenomena.
cites work: Q4942086
cites work: Analytical solutions to the backward Kolmogorov PDE via an adiabatic approximation to the Schrödinger PDE
cites work: A discussion on embedding the Black-Scholes option pricing model in a quantum physics setting
cites work: A Black-Scholes Schrödinger option price: `bit' versus `qubit'
cites work: The Black–Scholes pricing formula in the quantum context
cites work: Q3426503
cites work: Contextual approach to quantum mechanics and the theory of the fundamental prespace
cites work: On Quantum-Like Probabilistic Structure of Mental Information
cites work: The principle of supplementarity: a contextual probabilistic viewpoint to complementarity, the interference of probabilities and incompatibility of variables in quantum mechanics
cites work: Quantum equilibria for macroscopic systems
cites work: Quantumlike representation of extensive form games: Probabilistic aspects
cites work: Can quantum information be processed by macroscopic systems?
cites work: Q5814635
cites work: Introduction to Econophysics
cites work: Q4220653
cites work: Martingales, nonlinearity, and chaos
cites work: Q4230831
cites work: Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach
cites work: Q5614773
DOI: 10.1016/J.JMAA.2008.04.072
description: scientific article; zbMATH DE number 5303214