Quantum Brownian oscillator for the stock market

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 t...

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Bibliographic Details
Published inarXiv.org
Main Authors Jeknić-Dugić, Jasmina, Sonja Radi\' c, Petrović, Igor, Arsenijević, Momir, Dugić, Miroljub
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.12.2018
Subjects
Brownian motion
Damping
Efficient markets
Hypotheses
Kurtosis
Markets
Mechanical properties
Pricing
Securities markets
Variation
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Summary: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.
ISSN:2331-8422