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Stochastic modelling of financial markets with differential information
Many of the fundamental results in mathematical finance are based on the assumption that all traders have access to exactly the same information, usually assumed to be the filtration generated by the history of stock prices or the history of the underlying Brownian motion. In the last fifteen years...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2024
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| _version_ | 1867613474029305856 |
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| access_status_str | Open Access |
| author | Damiani, F V |
| author2 | Ouwehand, Peter |
| author_browse | Damiani, F V Ouwehand, Peter |
| author_facet | Ouwehand, Peter Damiani, F V |
| author_sort | Damiani, F V |
| collection | Thesis |
| description | Many of the fundamental results in mathematical finance are based on the assumption that all traders have access to exactly the same information, usually assumed to be the filtration generated by the history of stock prices or the history of the underlying Brownian motion. In the last fifteen years or so, many articles in the financial mathematics literature have been concerned with using techniques of stochastic calculus to model financial markets in which different traders have access to different levels of information. This thesis aims to provide a coherent account of the various approaches that have been used to model financial markets with heterogeneously informed agents. Part I of the thesis presents a description of the two branches of stochastic analysis that are required to understand the financial models: namely, Malliavin's calculus and enlargements of filtrations. Part II applies the mathematical results of Part I to provide a comprehensive presentation of the various financial models that have been introduced in the literature. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/39893 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:36:43.156Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/39893 Stochastic modelling of financial markets with differential information Damiani, F V Ouwehand, Peter Mathematics and Applied Mathematics Many of the fundamental results in mathematical finance are based on the assumption that all traders have access to exactly the same information, usually assumed to be the filtration generated by the history of stock prices or the history of the underlying Brownian motion. In the last fifteen years or so, many articles in the financial mathematics literature have been concerned with using techniques of stochastic calculus to model financial markets in which different traders have access to different levels of information. This thesis aims to provide a coherent account of the various approaches that have been used to model financial markets with heterogeneously informed agents. Part I of the thesis presents a description of the two branches of stochastic analysis that are required to understand the financial models: namely, Malliavin's calculus and enlargements of filtrations. Part II applies the mathematical results of Part I to provide a comprehensive presentation of the various financial models that have been introduced in the literature. 2024-06-18T11:53:28Z 2024-06-18T11:53:28Z 2008 2024-06-18T11:39:50Z Thesis / Dissertation Masters MSc http://hdl.handle.net/11427/39893 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Damiani, F V Stochastic modelling of financial markets with differential information |
| thesis_degree_str | Master's |
| title | Stochastic modelling of financial markets with differential information |
| title_full | Stochastic modelling of financial markets with differential information |
| title_fullStr | Stochastic modelling of financial markets with differential information |
| title_full_unstemmed | Stochastic modelling of financial markets with differential information |
| title_short | Stochastic modelling of financial markets with differential information |
| title_sort | stochastic modelling of financial markets with differential information |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/39893 |
| work_keys_str_mv | AT damianifv stochasticmodellingoffinancialmarketswithdifferentialinformation |