The Kurzweil integral in financial market modeling
Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken int...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2016-07-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/141/2/mb141_2_9.pdf |
| _version_ | 1818277587510624256 |
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| author | Pavel Krejčí Harbir Lamba Giselle Antunes Monteiro Dmitrii Rachinskii |
| author_facet | Pavel Krejčí Harbir Lamba Giselle Antunes Monteiro Dmitrii Rachinskii |
| author_sort | Pavel Krejčí |
| collection | DOAJ |
| description | Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities both in time and in memory. The main analytical tool is the Kurzweil integral formalism, and the main result proves the well-posedness of the process in the space of right-continuous regulated functions. |
| first_indexed | 2024-12-12T23:03:55Z |
| format | Article |
| id | doaj.art-53fc715777734c858ffd1710aba89a20 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-12-12T23:03:55Z |
| publishDate | 2016-07-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-53fc715777734c858ffd1710aba89a202022-12-22T00:08:45ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362016-07-01141226128610.21136/MB.2016.18MB.2016.18The Kurzweil integral in financial market modelingPavel KrejčíHarbir LambaGiselle Antunes MonteiroDmitrii RachinskiiCertain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities both in time and in memory. The main analytical tool is the Kurzweil integral formalism, and the main result proves the well-posedness of the process in the space of right-continuous regulated functions.http://mb.math.cas.cz/full/141/2/mb141_2_9.pdf hysteresis Prandtl-Ishlinskii operator Kurzweil integral market model |
| spellingShingle | Pavel Krejčí Harbir Lamba Giselle Antunes Monteiro Dmitrii Rachinskii The Kurzweil integral in financial market modeling Mathematica Bohemica hysteresis Prandtl-Ishlinskii operator Kurzweil integral market model |
| title | The Kurzweil integral in financial market modeling |
| title_full | The Kurzweil integral in financial market modeling |
| title_fullStr | The Kurzweil integral in financial market modeling |
| title_full_unstemmed | The Kurzweil integral in financial market modeling |
| title_short | The Kurzweil integral in financial market modeling |
| title_sort | kurzweil integral in financial market modeling |
| topic | hysteresis Prandtl-Ishlinskii operator Kurzweil integral market model |
| url | http://mb.math.cas.cz/full/141/2/mb141_2_9.pdf |
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