A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions

Sameerah Jamal; Rivoningo Maphanga; Sameerah Jamal; Rivoningo Maphanga

doi:10.3934/math.2024214

AIMS Mathematics

2024, Volume 9, Issue 2: 4326-4336. doi: 10.3934/math.2024214

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A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions

Sameerah Jamal ^{1,2
,
,},
Rivoningo Maphanga ¹

1.
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 Africa

Received: 11 August 2023 Revised: 16 November 2023 Accepted: 16 November 2023 Published: 16 January 2024
MSC : 35K05, 35K15, 37C79

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.
- constant elasticity of variance,
- Lie symmetries,
- convolution,
- boundary conditions
Citation: Sameerah Jamal, Rivoningo Maphanga. A progressive approach to solving a generalized CEV-type model by applying symmetry-invariant surface conditions[J]. AIMS Mathematics, 2024, 9(2): 4326-4336. doi: 10.3934/math.2024214

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Abstract

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.

References

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