Invariant approach to optimal investment–consumption problem: the constant elasticity of variance (CEV) model. (30th June 2016)

• Record Type: Journal Article
• Authors: Bakkaloglu, Ahmet; Aziz, Taha; Fatima, Aeeman; Mahomed, F.M.; Khalique, Chaudry Masood
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 5(2017)
• Page Start: 1382
• Page End: 1395
• Publication Date: 2016-06-30
• Subjects: invariant approach -- lie symmetry -- investment–consumption problem -- CEV model -- fundamental solutions -- Cauchy problem; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4060
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The optimal investment–consumption problem under the constant elasticity of variance (CEV) model is solved using the invariant approach. Firstly, the invariance criteria for scalar linear second‐order parabolic partial differential equations in two independent variables are reviewed. The criteria is then employed to reduce the CEV model to one of the four Lie canonical forms. It is found that the invariance criteria help in transforming the original equation to the second Lie canonical form and with a proper parameter selection; the required transformation converts the original equation to the first Lie canonical form that is the heat equation. As a consequence, we find some new classes of closed‐form solutions of the CEV model for the case of reduction into heat equation and also into second Lie canonical form. The closed‐form analytical solution of the Cauchy initial value problems for the CEV model under investigation is also obtained. Copyright © 2016 John Wiley & Sons, Ltd.