Application of Bohmian Mechanics to Dynamics of Prices of Shares: Stochastic Model of Bohm–Vigier from Properties of Price Trajectories

Abstract

We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Through comparing properties of trajectories we come to the conclusion that the only possibility to proceed with real financial data is to apply the stochastic version of the pilot wave theory-the model of Bohm-Vigier.

Application of Theory of Quantum Instruments to Psychology: Combination of Question Order Effect with Response Replicability Effect

“…Recent years have been characterized by a real explosion of interest to applications of quantum measurement theory and other parts of quantum theory outside of physics, especially in psychology, decision-making, economics, finances, and social science, as well as in genetics and molecular biology. (The work of [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 ] for some representative papers.) We call the corresponding models quantum-like.…”

Fisher information and quantum potential well model for finance

“…A second area concerns the development of a theoretical model that is able to encompass the essential features of real financial system which is characterized by such PDF. Financial economics borrows results in statistical physics [3], and in addition to statistical-mechanical description, a quantum mechanical representation has also emerged [4][5][6][7][8]. Unfortunately, the constructing of quantum theory for finances often reduces to direct postulation of Schrödinger equation and its subsequent solution under some entry conditions.…”

Emergent quantum mechanics of finances

“…In contrast to external force function Φ the quantum potential depending on probability amplitude has to reflect the influence of traders expectations or 'mental ψ-field' in interpretation of [5] and [4]. Due to modern electronic communications the financial agents being almost instantly informed of all price movements may change their mind about a market, i.e.…”