Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics

Date

2005-05-01

Author

Naicker, V
Andriopoulos, K
Leach, PGL

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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.

Subject Keywords

Mathematical Physics, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/66495

Journal

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS

DOI

https://doi.org/10.2991/jnmp.2005.12.2.8

Collections

Department of Physics, Article

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Citation Formats

V. Naicker, K. Andriopoulos, and P. Leach, “Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics,” JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, pp. 268–283, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66495.