Schrödinger type equation for subjective identification of supply and demand

Makowski, Marcin; Piotrowski, Edward W.; Sładkowski, Jan

doi:10.1016/j.physa.2019.01.068

“…This allows for its interpretation as the demand risk operator and we have a connection between risk and information associated with strategy: Minimal information content of a market supply/demand strategy is equal to the sum of the related supply and demand risk. Full details of the economic interpretation of this equation can be found in [1].…”

Section: Schrödinger-like Equation From the Principle Of Minimum Fish...mentioning

confidence: 99%

“…In Section 2, we recall the definition of Fisher information. For clarity in the results presented, in the next Section 3, we present the derivation of the mentioned Schrödinger-type equation contained in [1]. Next, we determine the Fisher information of the eigenvector (market strategy) of the oscillator.…”

Section: Introductionmentioning

confidence: 99%

Transactional Interpretation for the Principle of Minimum Fisher Information

Makowski,

Piotrowski,

Frąckiewicz

et al. 2022

Preprint

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The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strategy with a fixed financial risk. Strategies of this type that minimize Fisher information overlap with the well-known eigenstates of a the quantum harmonic oscillator. The analytical extension of this field of strategy to the complex vector space (traditional for quantum mechanics) suggests the study of the interference of the oscillator eigenstates in terms of their minimization of Fisher information. It is revealed that the minimum value of Fisher information of the superposition of the two strategies being the ground state and the second excited state of the oscillator, has Fisher information less than the ground state of the oscillator. Similarly, less information is obtained for the system of strategies (the oscillator eigenstates) randomized by the Gibbs distribution. We distinguish two different views on the description of Fisher information. One of them, the classical, is based on the value of Fisher information.

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“…One direction of such analysis is the description of market transactions in terms of supply and demand curves [ 6 , 7 , 8 , 9 , 10 ]. In this approach, quantum strategies are vectors in a certain Hilbert space and can be interpreted as superpositions of trading decisions.…”

Section: Introductionmentioning

confidence: 99%

“…The above formalism can be presented in an elegant way with the help of the Wigner functions defined on the common domain of variables x and y (the phase space):

Conditional (fixed public price for buying or selling) demand and supply curves are depicted by the graphs of the following CDFs :

where c denotes the price of the good in question. This formalism is convenient for analyzing exceptions to the classical laws of supply and demand (Giffen goods), which we can view as negative probabilities [ 10 ].…”

Section: Introductionmentioning

confidence: 99%

Transactional Interpretation and the Generalized Poisson Distribution

Makowski

¹

,

Piotrowski

²

2022

Entropy

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The aim of this paper is to study the quantum-like approach to the description of the market in the context of the principle of minimum Fisher information. We wish to investigate the validity of using squeezed coherent states as market strategies. For this purpose, we focus on the representation of any squeezed coherent state with respect to the basis of the eigenvectors of the observable of market risk. We derive a formula for the probability of being the squeezed coherent state in one of these states. The distribution that we call generalized Poisson establishes the relation between the squeezed coherent states and their description in the language of risk in quantum terms. We provide a formula specifying the total risk of squeezed coherent strategy. Then, we propose a risk of risk concept that is in fact the second central moment of the generalized Poisson distribution. This is an important numerical characterization of squeezed coherent strategies. We provide its interpretations on the basis of the uncertainty relation for time and energy.

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“…In Section 2, we recall the definition of Fisher information. For clarity in the results presented, in the next Section 3, we present the derivation of the mentioned Schrödinger-type equation contained in [5]. Next, we determine the Fisher information of the eigenvector (market strategy) of the oscillator.…”

Section: Introductionmentioning

confidence: 99%

Transactional Interpretation for the Principle of Minimum Fisher Information

Makowski

¹

,

Piotrowski

²

,

Frąckiewicz

³

et al. 2021

Entropy

Self Cite

View full text Add to dashboard Cite

The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strategy with a fixed financial risk. Strategies of this type that minimize Fisher information overlap with the well-known eigenstates of a the quantum harmonic oscillator. The analytical extension of this field of strategy to the complex vector space (traditional for quantum mechanics) suggests the study of the interference of the oscillator eigenstates in terms of their minimization of Fisher information. It is revealed that the minimum value of Fisher information of the superposition of the two strategies being the ground state and the second excited state of the oscillator, has Fisher information less than the ground state of the oscillator. Similarly, less information is obtained for the system of strategies (the oscillator eigenstates) randomized by the Gibbs distribution. We distinguish two different views on the description of Fisher information. One of them, the classical, is based on the value of Fisher information. The second, we call it transactional, expresses Fisher information from the perspective of the constant risk of market strategies. The orders of the market strategies derived from these two descriptions are different. From a market standpoint, minimizing Fisher information is equivalent to minimizing risk.

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Schrödinger type equation for subjective identification of supply and demand

Cited by 5 publications

References 22 publications

Transactional Interpretation for the Principle of Minimum Fisher Information

Transactional Interpretation for the Principle of Minimum Fisher Information

Transactional Interpretation and the Generalized Poisson Distribution

Transactional Interpretation for the Principle of Minimum Fisher Information

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