A discrete-time model that weakly converges to a continuous-time geometric Brownian motion with Markov switching drift rate
2024 (English)In: Frontiers in Applied Mathematics and Statistics, E-ISSN 2297-4687, Vol. 10, article id 1450581Article in journal (Refereed) Published
Abstract [en]
This research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 x 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.
Place, publisher, year, edition, pages
Frontiers Media S.A., 2024. Vol. 10, article id 1450581
Keywords [en]
geometric Brownian motion, Markov switching, discrete-time multiplicative approximation, equivalent martingale measure, incomplete financial market
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-115354DOI: 10.3389/fams.2024.1450581ISI: 001285525400001Scopus ID: 2-s2.0-8520058944OAI: oai:DiVA.org:oru-115354DiVA, id: diva2:1890386
Funder
Swedish Foundation for Strategic Research, UKR24-0004
Note
The author(s) declare financial support was received for the research, authorship, and/or publication of this article. YM was supported by the Swedish Foundation for Strategic Research (Grant No. UKR24-0004), the by Japan Science and Technology Agency CREST JPMJCR2115, and ToppForsk (Project No. 274410) of the Research Council of Norway with the title STORM: Stochastics for Time-Space Risk Models.
2024-08-192024-08-192024-08-19Bibliographically approved