A discrete-time model that weakly converges to a continuous-time geometric Brownian motion with Markov switching drift rate
2024 (engelsk)Inngår i: Frontiers in Applied Mathematics and Statistics, E-ISSN 2297-4687, Vol. 10, artikkel-id 1450581Artikkel i tidsskrift (Fagfellevurdert) 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.
sted, utgiver, år, opplag, sider
Frontiers Media S.A., 2024. Vol. 10, artikkel-id 1450581
Emneord [en]
geometric Brownian motion, Markov switching, discrete-time multiplicative approximation, equivalent martingale measure, incomplete financial market
HSV kategori
Identifikatorer
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
Forskningsfinansiär
Swedish Foundation for Strategic Research, UKR24-0004
Merknad
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.
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