# 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

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topKrejčí, 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 -

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