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Symmetry reductions of a Hamilton-Jacobi-Bellman equation arising in financial mathematics. (English) Zbl 1080.35163
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:
35Q80Appl. of PDE in areas other than physics (MSC2000)
91B28Finance etc. (MSC2000)
35R60PDEs with randomness, stochastic PDE
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