Symmetry Reductions of a Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics

DOI

10.2991/jnmp.2005.12.2.8How to use a DOI?

Abstract

We determine the solutions of a nonlinear Hamilton-Jacobi-Bellman equation which arises in the modelling of mean-variance hedging subject to a terminal condition. Firstly we establish those forms of the equation which admit the maximal number of Lie point symmetries and then examine each in turn. We show that the Lie method is only suitable for an equation of maximal symmetry. We indicate the applicability of the method to cases in which the parametric function depends also upon the time.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V. Naicker
AU  - K. Andriopoulos
AU  - P.G.L. Leach
PY  - 2005
DA  - 2005/05/01
TI  - Symmetry Reductions of a Hamilton-Jacobi-Bellman Equation Arising in Financial Mathematics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 268
EP  - 283
VL  - 12
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.2.8
DO  - 10.2991/jnmp.2005.12.2.8
ID  - Naicker2005
ER  -