Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion

Taranto, Aldo ORCID: https://orcid.org/0000-0001-6763-4997 and Addie, Ron ORCID: https://orcid.org/0000-0002-6664-8462 and Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X (2022) Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion. Journal of Applied Probability and Statistics, 17 (1). pp. 101-133. ISSN 1930-6792


Abstract

Bi-directional grid constrained (BGC) stochastic processes (BGCSPs) are identified as a variant rather than a special case of the multi-skew Brownian motion (M-SBM). This is because they have their own complexities, such as the barriers being hidden (not known in advance) and not necessarily constant over time. We provide a M-SBM theoretical framework and also a simulation framework to elaborate deeper properties of BGCSPs. The simulation framework is then applied by generating numerous simulations of the constrained paths and the results are analysed. BGCSPs have applications in finance and indeed many other fields requiring graduated constraining, from both above and below the initial starting position.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty/School / Institute/Centre: Current – Faculty of Health, Engineering and Sciences - School of Mathematics, Physics and Computing (1 Jan 2022 -)
Faculty/School / Institute/Centre: Current – Faculty of Health, Engineering and Sciences - School of Mathematics, Physics and Computing (1 Jan 2022 -)
Date Deposited: 12 May 2022 02:40
Last Modified: 12 May 2022 02:40
Uncontrolled Keywords: Wiener Processes, Ito Processes, Reflecting Barriers, Stochastic Differential Equation (SDE), Stopping Times, First Passage Time (FPT), Multi-Skew Brownian Motion (M-SBM)
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling
49 MATHEMATICAL SCIENCES > 4905 Statistics > 490503 Computational statistics
49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
URI: http://eprints.usq.edu.au/id/eprint/48455

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