Bohmian mechanics for financial processes

Choustova, Olga

doi:10.1080/09500340410001664124

Cited by 9 publications

(12 citation statements)

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“…We repeat shortly the Bohmian model for the financial market proposed in [11][12][13]. Let us consider a mathematical model in that a huge number of agents of the financial market interact with one another and take into account external economic (as well as political, social and even meteorological) conditions in order to determine the price to buy or sell financial assets.…”

Section: Price Phase Space Modeling Of Financial Energymentioning

confidence: 99%

Quantum probability and financial market

Choustova¹

2009

Information Sciences

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Section: Price Phase Space Modeling Of Financial Energymentioning

confidence: 99%

Quantum probability and financial market

Choustova¹

2009

Information Sciences

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“…Many such interpretations have indeed been tried, and it turned out that the most efficient is the representation of each complex values z = ψ(x) as a pair (ρ, φ) for which z = ρ • exp(i • φ); see, e.g., [8,9,10,11]. This representation is called Bohmian, because of the physicist and philosopher David Bohm who used ρ and φ to provide a physical interpretation of the wave function; see, e.g., [6,7]; thus, the corresponding applications to econometrics are knows as Bohmian econometrics.…”

Section: The Desired Linear Combination Becomes a Complex Numbermentioning

confidence: 99%

Why Bohmian Approach to Quantum Econometrics: An Algebraic Explanation

Kreinovich

Kosheleva

Sriboonchitta

2020

Algebraic Techniques and Their Use in Describing and Processing Uncertainty

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Many equations in economics and finance are very complex. As a result, existing methods of solving these equations are very complicated and timeconsuming. In many practical situations, more efficient algorithms for solving new complex equations appear when it turns out that these equations can be reduced to equations from other application areas-equations for which more efficient algorithms are already known. It turns out that some equations in economics and finance can be reduced to equations from physics-namely, from quantum physics. The resulting approach for solving economic equations is known as quantum econometrics. In quantum physics, the main objects are described by complex numbers; so, to have a reduction, we need to come up with an economic interpretation of these complex numbers. It turns out that in many cases, the most efficient interpretation comes when we separately interpret the absolute value (modulus) and the phase of each corresponding quantum number; the resulting techniques are known as Bohmian econometrics. In this paper, we use an algebraic approach-namely, the idea of invariance and symmetries-to explain why such an interpretation is empirically the best. 1 Formulation of the Problem Quantum econometrics: a brief reminder. Economic and financial phenomena are very complex. As a result, many corresponding equations are very difficult to solve.

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“…We repeat shortly the Bohmian model for the financial market which was proposed in [3,4]. We start with the classical model for the price-dynamics.…”

Section: Price-space Classical Modelmentioning

confidence: 99%

“…We shall show that it seems that only such a stochastic model can provide an adequate description of the real financial data, cf. with applications to finance of the deterministic Bohmian model [3,4].…”

Section: Introductionmentioning

confidence: 99%