Quantum probability and financial market

Choustova, Olga

doi:10.1016/j.ins.2008.07.001

Cited by 26 publications

(22 citation statements)

References 39 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Ozawa

Khrennikov

2019

Entropy

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Recently, quantum formalism started to be actively used outside of quantum physics: in psychology, decision-making, economics, finances, and social science. Human psychological behavior is characterized by a few basic effects; one of them is the question order effect (QOE). This effect was successfully modeled (Busemeyer–Wang) by representing questions A and B by Hermitian observables and mental-state transformations (back action of answering) by orthogonal projectors. However, then it was demonstrated that such representation cannot be combined with another psychological effect, known as the response replicability effect (RRE). Later, this no-go result was generalized to representation of questions and state transformations by quantum instruments of the atomic type. In light of these results, the possibility of using quantum formalism in psychology was questioned. In this paper, we show that, nevertheless, the combination of the QOE and RRE can be modeled within quantum formalism, in the framework of theory of non-atomic quantum instruments.

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Section: Introductionmentioning

confidence: 99%

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

Ozawa

Khrennikov

2019

Entropy

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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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“…Through the works of Segal [ 19 ] and Bagarello [ 20 , 21 ] and Haven et al [ 22 ], amongst others, the usefulness of quantum mechanics in their applications to finance was better understood. It was Choustova [ 23 ] who first proposed to further analyze financial behavior using Bohmian quantum mechanics. Tahmasebi [ 24 ] and Shen et al [ 25 ] used Choustova’s idea to show that historical (public) information of an asset could be stored in a quantum potential governing that asset (within a particular period of time).…”

Section: Introductionmentioning

confidence: 99%

Using the Quantum Potential in Elementary Portfolio Management: Some Initial Ideas

Khaksar

Haven

Nasiri

et al. 2021

Entropy

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Owing to the globalization of the economy, the concept of entangled markets started to form, and this occurrence has smoothed the entrance of quantum mechanics into behavioral finance. In this manuscript, we introduce quantum risk and perform an analysis on portfolio optimization by controlling the quantum potential. We apply this method to eight major indices and construct a portfolio with a minimum quantum risk. The results show quantum risk has a power law behavior with a time-scale just as a standard deviation with different exponents.

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Quantum probability and financial market

Cited by 26 publications

References 39 publications

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

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

Why Bohmian Approach to Quantum Econometrics: An Algebraic Explanation

Using the Quantum Potential in Elementary Portfolio Management: Some Initial Ideas

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