The Kurzweil integral in financial market modeling

Pavel Krejčí; Harbir Lamba; Giselle Antunes Monteiro; Dmitrii Rachinskii

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 2, page 261-286
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Krejčí, Pavel, et al. "The Kurzweil integral in financial market modeling." Mathematica Bohemica 141.2 (2016): 261-286. <http://eudml.org/doc/276984>.

@article{Krejčí2016,
abstract = {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.},
author = {Krejčí, Pavel, Lamba, Harbir, Monteiro, Giselle Antunes, Rachinskii, Dmitrii},
journal = {Mathematica Bohemica},
keywords = {hysteresis; Prandtl-Ishlinskii operator; Kurzweil integral; market model},
language = {eng},
number = {2},
pages = {261-286},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Kurzweil integral in financial market modeling},
url = {http://eudml.org/doc/276984},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Lamba, Harbir
AU - Monteiro, Giselle Antunes
AU - Rachinskii, Dmitrii
TI - The Kurzweil integral in financial market modeling
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 2
SP - 261
EP - 286
AB - 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.
LA - eng
KW - hysteresis; Prandtl-Ishlinskii operator; Kurzweil integral; market model
UR - http://eudml.org/doc/276984
ER -

References

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