Quantum Brownian motion model for the stock market

TL;DR

This paper introduces a quantum mechanics-inspired model for the stock market, representing stocks as quantum oscillators and analyzing market irrationality and non-Markovian behaviors through quantum Brownian motion, challenging classical assumptions.

Contribution

It develops a novel econophysics framework using quantum concepts to model stock market dynamics and irrationality, providing new insights into market behaviors beyond classical models.

Findings

Quantum model captures fat-tail phenomena in stock returns.

Non-Markovian behaviors are evident in real stock data.

Quantum approach offers a new perspective on market inefficiencies.

Abstract

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.