Transactional Interpretation and the Generalized Poisson Distribution
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/10/1416 |
| _version_ | 1797473454400733184 |
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| author | Marcin Makowski Edward Wiktor Piotrowski |
| author_facet | Marcin Makowski Edward Wiktor Piotrowski |
| author_sort | Marcin Makowski |
| collection | DOAJ |
| description | 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 <i>risk of risk</i> 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. |
| first_indexed | 2024-03-09T20:14:43Z |
| format | Article |
| id | doaj.art-92a212b634c44b65bea533ba39a137b3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:14:43Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-92a212b634c44b65bea533ba39a137b32023-11-24T00:03:22ZengMDPI AGEntropy1099-43002022-10-012410141610.3390/e24101416Transactional Interpretation and the Generalized Poisson DistributionMarcin Makowski0Edward Wiktor Piotrowski1Faculty of Physics, Department of Mathematical Methods in Physics, University of Białystok, Ul. Ciołkowskiego 1L, 15-245 Białystok, PolandFaculty of Physics, Department of Mathematical Methods in Physics, University of Białystok, Ul. Ciołkowskiego 1L, 15-245 Białystok, PolandThe 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 <i>risk of risk</i> 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.https://www.mdpi.com/1099-4300/24/10/1416squeezed coherent statesFisher informationFourier transformSchrödinger-like equationmarketrisk |
| spellingShingle | Marcin Makowski Edward Wiktor Piotrowski Transactional Interpretation and the Generalized Poisson Distribution Entropy squeezed coherent states Fisher information Fourier transform Schrödinger-like equation market risk |
| title | Transactional Interpretation and the Generalized Poisson Distribution |
| title_full | Transactional Interpretation and the Generalized Poisson Distribution |
| title_fullStr | Transactional Interpretation and the Generalized Poisson Distribution |
| title_full_unstemmed | Transactional Interpretation and the Generalized Poisson Distribution |
| title_short | Transactional Interpretation and the Generalized Poisson Distribution |
| title_sort | transactional interpretation and the generalized poisson distribution |
| topic | squeezed coherent states Fisher information Fourier transform Schrödinger-like equation market risk |
| url | https://www.mdpi.com/1099-4300/24/10/1416 |
| work_keys_str_mv | AT marcinmakowski transactionalinterpretationandthegeneralizedpoissondistribution AT edwardwiktorpiotrowski transactionalinterpretationandthegeneralizedpoissondistribution |