A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions
In this paper, we examine a type of constant elasticity of variance model that is subject to its terminal condition. We prove that certain transformations may be applied to obtain a simpler equation that has known solution processes. Four cases are obtained that play a role in specifying the many un...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024214?viewType=HTML |
| _version_ | 1797323877305548800 |
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| author | Sameerah Jamal Rivoningo Maphanga |
| author_facet | Sameerah Jamal Rivoningo Maphanga |
| author_sort | Sameerah Jamal |
| collection | DOAJ |
| description | In this paper, we examine a type of constant elasticity of variance model that is subject to its terminal condition. We prove that certain transformations may be applied to obtain a simpler equation that has known solution processes. Four cases are obtained that play a role in specifying the many unknown parameters of the model. The corresponding terminal condition is transformed into an initial condition, and we then demonstrate how to solve this Cauchy problem by using Lie symmetries and Poisson's formula. Finally, we examine the behaviour of the obtained solutions. |
| first_indexed | 2024-03-08T05:34:29Z |
| format | Article |
| id | doaj.art-f23098004bb34b939c4a7d10c921163f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:34:29Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f23098004bb34b939c4a7d10c921163f2024-02-06T01:18:00ZengAIMS PressAIMS Mathematics2473-69882024-01-01924326433610.3934/math.2024214A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditionsSameerah Jamal0Rivoningo Maphanga11. School of Mathematics, University of the Witwatersrand, Johannesburg 2001, South Africa 2. DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg 2001, South Africa1. School of Mathematics, University of the Witwatersrand, Johannesburg 2001, South AfricaIn this paper, we examine a type of constant elasticity of variance model that is subject to its terminal condition. We prove that certain transformations may be applied to obtain a simpler equation that has known solution processes. Four cases are obtained that play a role in specifying the many unknown parameters of the model. The corresponding terminal condition is transformed into an initial condition, and we then demonstrate how to solve this Cauchy problem by using Lie symmetries and Poisson's formula. Finally, we examine the behaviour of the obtained solutions.https://www.aimspress.com/article/doi/10.3934/math.2024214?viewType=HTMLconstant elasticity of variancelie symmetriesconvolutionboundary conditions |
| spellingShingle | Sameerah Jamal Rivoningo Maphanga A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions AIMS Mathematics constant elasticity of variance lie symmetries convolution boundary conditions |
| title | A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions |
| title_full | A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions |
| title_fullStr | A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions |
| title_full_unstemmed | A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions |
| title_short | A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions |
| title_sort | progressive approach to solving a generalized cev type model by applying symmetry invariant surface conditions |
| topic | constant elasticity of variance lie symmetries convolution boundary conditions |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024214?viewType=HTML |
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