Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

Tanki Motsepa; Taha Aziz; Aeeman Fatima; Chaudry Masood Khalique

doi:10.1515/phys-2018-0006

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

Tanki Motsepa, Taha Aziz^*, Aeeman Fatima, Chaudry Masood Khalique

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Original language	English
Pages (from-to)	31-36
Number of pages	6
Journal	Open Physics
Volume	16
Issue number	1
DOIs	https://doi.org/10.1515/phys-2018-0006
State	Published - 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 T. Motsepa et al. 2018.

Keywords

CEV model
Conservation laws
Group-invariant solution
Lie point symmetries
Terminal condition

ASJC Scopus subject areas

General Physics and Astronomy

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10.1515/phys-2018-0006

Cite this

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title = "Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics",

abstract = "The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.",

keywords = "CEV model, Conservation laws, Group-invariant solution, Lie point symmetries, Terminal condition",

author = "Tanki Motsepa and Taha Aziz and Aeeman Fatima and Khalique, \{Chaudry Masood\}",

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AU - Motsepa, Tanki

AU - Aziz, Taha

AU - Fatima, Aeeman

AU - Khalique, Chaudry Masood

PY - 2018

Y1 - 2018

N2 - The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

AB - The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

KW - CEV model

KW - Conservation laws

KW - Group-invariant solution

KW - Lie point symmetries

KW - Terminal condition

UR - https://www.scopus.com/pages/publications/85043591937

U2 - 10.1515/phys-2018-0006

DO - 10.1515/phys-2018-0006

M3 - Article

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ER -

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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