The Kurzweil integral in financial market modeling

0459263 - MÚ 2017 RIV CZ eng J - Journal Article
Krejčí, Pavel - Lamba, H. - Monteiro, Giselle Antunes - Rachinskii, D.
The Kurzweil integral in financial market modeling.
Mathematica Bohemica. Roč. 141, č. 2 (2016), s. 261-286. ISSN 0862-7959
R&D Projects: GA ČR(CZ) GA15-12227S
Institutional support: RVO:67985840
Keywords : hysteresis * Prandtl-Ishlinskii operator * Kurzweil integral
OECD category: Pure mathematics
http://hdl.handle.net/10338.dmlcz/145715

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.
Permanent Link: http://hdl.handle.net/11104/0259487