We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ 3 could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on the regions of the state space, this manifold is either a dispersal one, an equivocal one or a 2D focal manifold. A pair of PDE's were derived for the focal part. Here we show that irrespective of the nature of this manifold, it has to satisfy this same set of PDE's.
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Pierre Bernhard (2006) studied this question.
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