Quantum model for the price dynamics: The problem of smoothness of trajectories

Choustova, Olga

doi:10.1016/j.jmaa.2008.04.072

Cited by 15 publications

(15 citation statements)

References 32 publications

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“…This was because of that the residential property values collected along the route given mainly depended on the effects of transportation systems and public parks in this work. Not surprisingly, the profile of the property price volatility along the routes of interest can be understood as a wave-like function of urban housing market system, similar to propagation of the transaction volume-price probability wave or the financial pilot wave [ 34 – 36 ]. Observed data on housing prices from government statistics datasets to depict the variance of the housing prices along designated routes taken from USGS National Map Viewer, as described in Fig 1 , for Boston, Milwaukee, Taipei and Tokyo were illustrated in Fig 5 , respectively.…”

Section: Resultsmentioning

confidence: 99%

“…It is possible to derive a new kind of volatility measure for house prices utilizing the quantum mechanics widely based on Schrödinger equations as well [ 33 – 35 ]. Taking into account for house prices and price changes, Bohmian model for behaviors of the financial market has been developed in teams of information perturbation of Hamiltonian equations [ 35 , 36 ].…”

Section: Introductionmentioning

confidence: 99%

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Lie symmetry analysis of the effects of urban infrastructures on residential property values

et al. 2021

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Due to the complexity of socio-economic-related issues, people thought of housing market as a chaotic nucleus situated at the intersection of neighboring sciences. It has been known that the dependence of house features on the residential property value can be estimated employing the well-established hedonic regression analysis method in teams of location characteristic, neighborhood characteristic and structure characteristic. However, to further assess the roles of urban infrastructures in housing markets, we proposed a new kind of volatility measure for house prices utilizing the Lie symmetry analysis of quantum theory based on Schrödinger equation, mainly focusing on the effects of transportation systems and public parks on residential property values. Based on the municipal open government data regularly collected for four cities, including Boston, Milwaukee, Taipei and Tokyo, and all spatial sampling sites were featured by United States Geological Survey (USGS) National Map, transportation and park were modelled as perturbations to the quantum states generated by the feature space in response to the environmental amenities with different spatial extents. In an attempt to ascertain the intrinsic impact of the location-dependent price information obtained, the similarity functions associated with the Schrödinger equation were considered to facilitate revealing the city amenities capitalizing into house prices. By examining the spatial spillover phenomena of house prices in the four cities investigated, it was found that the mass transit systems and the public green lands possessed the infinitesimal generators of Lie point symmetries Y2 and Y5, respectively. Compared statistically with the common performance criteria, including mean absolute error (MAE), mean squared error (MSE) and, root mean squared error (RMSE) obtained by hedonic pricing model, the Lie symmetry analysis of the Schrödinger equation approach developed herein was successfully carried out. The invariant-theoretical characterizations of economics-related phenomena are consonant with the observed residential property values of the cities internationally, ultimately leading to develop a new perspective in the global financial architecture.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis of the effects of urban infrastructures on residential property values

et al. 2021

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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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“…There have been applications of pilot wave theory to finance. See Khrennikov [5,6]; Choustova [19]; Haven and Khrennikov [20] and Haven [21]. An important element in this approach to finance is that borrowing from pilot-wave theory allows for a formalism, which we could call, information dynamics.…”

Section: Introductionmentioning

confidence: 99%

Using Empirical Data to Estimate Potential Functions in Commodity Markets: Some Initial Results

Shen

Haven

2017

Int J Theor Phys

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This paper focuses on estimating real and quantum potentials from financial commodities. The log returns of six common commodities are considered. We find that some phenomena, such as the vertical potential walls and the time scale issue of the variation on returns, also exists in commodity markets. By comparing the quantum and classical potentials, we attempt to demonstrate that the information within these two types of potentials is different. We believe this empirical result is consistent with the theoretical assumption that quantum potentials (when embedded into social science contexts) may contain some social cognitive or market psychological information, while classical potentials mainly reflect 'hard' market conditions. We also compare the two potential forces and explore their relationship by simply estimating the Pearson correlation between them. The Medium or weak interaction effect may indicate that the cognitive system among traders may be affected by those 'hard' market conditions.

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Quantum model for the price dynamics: The problem of smoothness of trajectories

Cited by 15 publications

References 32 publications

Lie symmetry analysis of the effects of urban infrastructures on residential property values

Lie symmetry analysis of the effects of urban infrastructures on residential property values

Why Bohmian Approach to Quantum Econometrics: An Algebraic Explanation

Using Empirical Data to Estimate Potential Functions in Commodity Markets: Some Initial Results

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