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Zbl 1080.35163
Naicker, V.; Andriopoulos, K.; Leach, P.G.L.
Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics. (English)
[J] J. Nonlinear Math. Phys. 12, No. 2, 268-283 (2005). ISSN 1402-9251; ISSN 1776-0852/e

Summary: 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. First 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 all equations of maximal symmetry. We indicate the applicability of the method to cases in which the parametric function depends also upon time.

MSC 2000:: *35Q80 Appl. of PDE in areas other than physics
91B28 Finance etc.
35R60 PDE with randomness

Keywords: diffusion equation; Black-Scholes equation; Hamilton-Jacobi-Bellman equation; mean-variance hedging; Lie point symmetries

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	Scientific prize winners of the ICM 2010
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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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Zentralblatt MATH Berlin [Germany]