Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Lie Analysis for Partial Differential Equations in Finance
Weather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Maths and Applied Maths
2020
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613170437193728 |
|---|---|
| access_status_str | Open Access |
| author | Nhangumbe, Clarinda Vitorino |
| author2 | Fredericks, Ebrahim |
| author_browse | Fredericks, Ebrahim Nhangumbe, Clarinda Vitorino |
| author_facet | Fredericks, Ebrahim Nhangumbe, Clarinda Vitorino |
| author_sort | Nhangumbe, Clarinda Vitorino |
| collection | Thesis |
| description | Weather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the mean reverting processes. As an example, the Ornstein Uhlenbeck process was proposed by Allen [3] to model yearly rainfall and by Unami et al. [52] to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equations (PDEs) that governs the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/31817 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:53.390Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | Department of Maths and Applied Maths |
| publisherStr | Department of Maths and Applied Maths |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/31817 Lie Analysis for Partial Differential Equations in Finance Nhangumbe, Clarinda Vitorino Fredericks, Ebrahim Canhanga , Betuel Lie symmetry analysis Ornstein-Uhlenbeck process Partial differential equations Rainfall index Weather derivatives Weather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the mean reverting processes. As an example, the Ornstein Uhlenbeck process was proposed by Allen [3] to model yearly rainfall and by Unami et al. [52] to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equations (PDEs) that governs the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions. 2020-05-06T12:57:35Z 2020-05-06T12:57:35Z 2019 2020-05-06T01:36:19Z Master Thesis Masters MSc https://hdl.handle.net/11427/31817 eng application/pdf Department of Maths and Applied Maths Faculty of Science |
| spellingShingle | Lie symmetry analysis Ornstein-Uhlenbeck process Partial differential equations Rainfall index Weather derivatives Nhangumbe, Clarinda Vitorino Lie Analysis for Partial Differential Equations in Finance |
| thesis_degree_str | Master's |
| title | Lie Analysis for Partial Differential Equations in Finance |
| title_full | Lie Analysis for Partial Differential Equations in Finance |
| title_fullStr | Lie Analysis for Partial Differential Equations in Finance |
| title_full_unstemmed | Lie Analysis for Partial Differential Equations in Finance |
| title_short | Lie Analysis for Partial Differential Equations in Finance |
| title_sort | lie analysis for partial differential equations in finance |
| topic | Lie symmetry analysis Ornstein-Uhlenbeck process Partial differential equations Rainfall index Weather derivatives |
| url | https://hdl.handle.net/11427/31817 |
| work_keys_str_mv | AT nhangumbeclarindavitorino lieanalysisforpartialdifferentialequationsinfinance |