Time evolution of pilot waves in finance

Gholizad, Amir (2025) Time evolution of pilot waves in finance. Masters thesis, Memorial University of Newfoundland.

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Abstract

This thesis explores the time evolution of quantum potentials in financial time series by developing novel technical indicators based on these quantum potentials. It starts with an introduction to de Broglie-Bohm’s pilot wave theory and its application in financial market analysis, detailing the derivation of quantum potential and quantum force from the probability density function (PDF) of logarithmic price changes. The research employs the sliding window technique to observe the temporal evolution of these quantum potentials and quantum forces and their corresponding features, while also examining correlations with traditional technical and statistical indicators. A significant part of the study involves comparing real financial markets to a theoretical Gaussian system defined by random walk theory, revealing notable differences in the number of equilibrium states and the shape of constraining walls. Strong correlations are found between the new features-particularly the length and depth of quantum potentials-and other indicators like standard deviation. Ultimately, this research advances the use of the pilot wave model in finance by introducing the “widening” behavior of quantum potentials and providing fully functional indicators for future research.

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