Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications

[1510.02013] Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:1510.02013 (math) [Submitted on 7 Oct 2015 ( v1 ), last revised 15 Dec 2015 (this version, v5)] Title: Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications Authors: Yusuke Morimoto , Makiko Sasada View a PDF of the paper titled Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications, by Yusuke Morimoto and Makiko Sasada View PDF HTML (experimental) Abstract: High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical methods. The authors found a special Lie algebraic structure on the vector fields in the major financial diffusion models. Using this structure, we can solve the flows associated with vector fields analytically and efficiently. Numerical examples show that our method saves the computation time drastically. Comments: 21 pages, 2 figures Subjects: Probability (math.PR) ; Computational Finance (q-fin.CP); Mathematical Finance (q-fin.MF) MSC classes: 65C05, 60G40 Cite as: arXiv:1510.02013 [math.PR] (or arXiv:1510.02013v5 [math.PR] for this version) https://doi.org/10.48550/arXiv.1510.02013 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Quantitative Finance (2017), 1105-1117 Related DOI : https://doi.org/10.1080/14697688.2016.1264618 Focus to learn more DOI(s) linking to related resources Submission history From: Makiko Sasada [ view email ] [v1] Wed, 7 Oct 2015 16:31:21 UTC (64 KB) [v2] Thu, 8 Oct 2015 14:54:15 UTC (64 KB) [v3] Fri, 9 Oct 2015 16:03:34 UTC (64 KB) [v4] Mon, 19 Oct 2015 15:35:10 UTC (58 KB) [v5] Tue, 15 Dec 2015 01:31:18 UTC (58 KB) Full-text links: Access Paper: View a PDF of the paper titled Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications, by Yusuke Morimoto and Makiko Sasada View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2015-10 Change to browse by: math q-fin q-fin.CP q-fin.MF References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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