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A note on the integrability of the classical portfolio selection model

Naicker, V and O'Hara, JG and Leach, PGL (2010) 'A note on the integrability of the classical portfolio selection model.' Applied Mathematics Letters, 23 (9). 1114 - 1119. ISSN 0893-9659

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Abstract

We revisit the classical Merton portfolio selection model from the perspective of integrability analysis. By an application of a nonlocal transformation the nonlinear partial differential equation for the two-asset model is mapped into a linear option valuation equation with a consumption dependent source term. This result is identical to the one obtained by Cox-Huang [J.C. Cox, C.-f. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, J. Econom. Theory 49 (1989) 33-88], using measure theory and stochastic integrals. The nonlinear two-asset equation is then analyzed using the theory of Lie symmetry groups. We show that the linearization is directly related to the structure of the generalized symmetries. © 2010 Elsevier Ltd. All rights reserved.

Item Type: Article
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 01 Feb 2013 15:50
Last Modified: 05 Feb 2019 03:15
URI: http://repository.essex.ac.uk/id/eprint/5445

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