Transactional Interpretation for the Principle of Minimum Fisher Information

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 ca...

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Autores principales: Marcin Makowski, Edward W. Piotrowski, Piotr Frąckiewicz, Marek Szopa
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Lenguaje:EN
Publicado: MDPI AG 2021
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spelling oai:doaj.org-article:69fd26d4260f4116a74fd66cf36fa3ae2021-11-25T17:29:52ZTransactional Interpretation for the Principle of Minimum Fisher Information10.3390/e231114641099-4300https://doaj.org/article/69fd26d4260f4116a74fd66cf36fa3ae2021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1464https://doaj.org/toc/1099-4300The 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.Marcin MakowskiEdward W. PiotrowskiPiotr FrąckiewiczMarek SzopaMDPI AGarticleFisher informationfourier transformSchrödinger-like equationmarketrisksupply and demandScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1464, p 1464 (2021)
institution DOAJ
collection DOAJ
language EN
topic Fisher information
fourier transform
Schrödinger-like equation
market
risk
supply and demand
Science
Q
Astrophysics
QB460-466
Physics
QC1-999
spellingShingle Fisher information
fourier transform
Schrödinger-like equation
market
risk
supply and demand
Science
Q
Astrophysics
QB460-466
Physics
QC1-999
Marcin Makowski
Edward W. Piotrowski
Piotr Frąckiewicz
Marek Szopa
Transactional Interpretation for the Principle of Minimum Fisher Information
description 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.
format article
author Marcin Makowski
Edward W. Piotrowski
Piotr Frąckiewicz
Marek Szopa
author_facet Marcin Makowski
Edward W. Piotrowski
Piotr Frąckiewicz
Marek Szopa
author_sort Marcin Makowski
title Transactional Interpretation for the Principle of Minimum Fisher Information
title_short Transactional Interpretation for the Principle of Minimum Fisher Information
title_full Transactional Interpretation for the Principle of Minimum Fisher Information
title_fullStr Transactional Interpretation for the Principle of Minimum Fisher Information
title_full_unstemmed Transactional Interpretation for the Principle of Minimum Fisher Information
title_sort transactional interpretation for the principle of minimum fisher information
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/69fd26d4260f4116a74fd66cf36fa3ae
work_keys_str_mv AT marcinmakowski transactionalinterpretationfortheprincipleofminimumfisherinformation
AT edwardwpiotrowski transactionalinterpretationfortheprincipleofminimumfisherinformation
AT piotrfrackiewicz transactionalinterpretationfortheprincipleofminimumfisherinformation
AT marekszopa transactionalinterpretationfortheprincipleofminimumfisherinformation
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