Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing
A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liqui...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/361785 |
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| author | Winter Sinkala Tembinkosi F. Nkalashe |
| author_facet | Winter Sinkala Tembinkosi F. Nkalashe |
| author_sort | Winter Sinkala |
| collection | DOAJ |
| description | A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model. |
| format | Article |
| id | doaj-art-3bb5d2a2902f434cb31df1f1f40b255e |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3bb5d2a2902f434cb31df1f1f40b255e2025-02-03T05:45:50ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/361785361785Lie Symmetry Analysis of a First-Order Feedback Model of Option PricingWinter Sinkala0Tembinkosi F. Nkalashe1Department of Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, South AfricaDepartment of Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, South AfricaA first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model.http://dx.doi.org/10.1155/2015/361785 |
| spellingShingle | Winter Sinkala Tembinkosi F. Nkalashe Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing Advances in Mathematical Physics |
| title | Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing |
| title_full | Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing |
| title_fullStr | Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing |
| title_full_unstemmed | Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing |
| title_short | Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing |
| title_sort | lie symmetry analysis of a first order feedback model of option pricing |
| url | http://dx.doi.org/10.1155/2015/361785 |
| work_keys_str_mv | AT wintersinkala liesymmetryanalysisofafirstorderfeedbackmodelofoptionpricing AT tembinkosifnkalashe liesymmetryanalysisofafirstorderfeedbackmodelofoptionpricing |