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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Dynamical Systems
Volume 10 - 2024 | doi: 10.3389/fams.2024.1450581
This article is part of the Research Topic Approximation Methods and Analytical Modeling Using Partial Differential Equations View all 12 articles

A discrete-time model that weakly converges to a continuous-time geometric Brownian motion with Markov switching drift rate

Provisionally accepted
Vitaliy Golomoziy Vitaliy Golomoziy 1*Yuliya Mishura Yuliya Mishura 1Kamil Kladívko Kamil Kladívko 2
  • 1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • 2 Örebro University, Örebro, Örebro, Sweden

The final, formatted version of the article will be published soon.

    This paper is devoted to studying a geometric Brownian motion with drift switching driven by 2 × 2 Markov chain. A discrete-time multiplicative approximation scheme was developed and its convergence in Skorokhod topology to the continuous-time geometric Brownian motion with switching has been proved. Furthermore, in a financial market where the discounted asset price follows a geometric Brownian motion with drift switching, market incompleteness was established, and multiple equivalent martingale measures were constructed.

    Keywords: Geometric Brownian motion, Markov switching, discrete-time multiplicative approximation, Equivalent martingale measure, Incomplete financial market

    Received: 17 Jun 2024; Accepted: 05 Jul 2024.

    Copyright: © 2024 Golomoziy, Mishura and Kladívko. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Vitaliy Golomoziy, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

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