ON THE SINGULARITIES OF AN IMPULSIVE DIFFERENTIAL GAME ARISING IN MATHEMATICAL FINANCE

Pierre Bernhard ()
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Pierre Bernhard: I3S, University of Nice-Sophia Antipolis and CNRS, France

International Game Theory Review (IGTR), 2006, vol. 08, issue 02, 219-229

Abstract: 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 ℝ3could 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.

Keywords: Differential games; robust control; impulse control; option pricing (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219198906000874

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