# Quantum Brownian oscillator for the stock market

## TL;DR

This paper models stock market fluctuations using quantum Brownian motion, exploring quantum effects that could challenge the classical efficient market hypothesis and offer new insights into market behavior.

## Contribution

It introduces a quantum Brownian oscillator model with the Caldeira-Leggett equation to analyze stock price deviations from classical predictions.

## Key findings

- Quantum regimes show deviations from classical market models.
- Varying damping and temperature simulate different economic scenarios.
- Quantum effects may explain anomalies not captured by classical theories.

## Abstract

We pursue the quantum-mechanical challenge to the efficient market hypothesis for the stock market by employing the quantum Brownian motion model. We utilize the quantum Caldeira-Leggett master equation as a possible phenomenological model for the stock-market-prices fluctuations while introducing the external harmonic field for the Brownian particle. Two quantum regimes are of particular interest: the exact regime as well as the approximate regime of the pure decoherence ("recoilless") limit of the Caldeira-Leggett equation. By calculating the standard deviation and the kurtosis for the particle's position observable, we can detect deviations of the quantum-mechanical behavior from the classical counterpart, which bases the efficient market hypothesis. By varying the damping factor, temperature as well as the oscillator's frequency, we are able to provide interpretation of different economic scenarios and possible situations that are not normally recognized by the efficient market hypothesis. Hence we recognize the quantum Brownian oscillator as a possibly useful model for the realistic behavior of stock prices.