AUTHOR=Golomoziy Vitaliy , Mishura Yuliya , Kladívko Kamil 

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

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1450581

DOI=10.3389/fams.2024.1450581

ISSN=2297-4687

ABSTRACT=<p>This research is devoted to studying a geometric Brownian motion with drift switching driven by a 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.</p>