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Further Calculations for the McKean Stochastic Game for a Spectrally Negative Lévy Process: From a Point to an Interval
Published online by Cambridge University Press: 14 July 2016
Abstract
Following Baurdoux and Kyprianou (2008) we consider the McKean stochastic game, a game version of the McKean optimal stopping problem (American put), driven by a spectrally negative Lévy process. We improve their characterisation of a saddle point for this game when the driving process has a Gaussian component and negative jumps. In particular, we show that the exercise region of the minimiser consists of a singleton when the penalty parameter is larger than some threshold and ‘thickens’ to a full interval when the penalty parameter drops below this threshold. Expressions in terms of scale functions for the general case and in terms of polynomials for a specific jump diffusion case are provided.
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- Research Article
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- Copyright © Applied Probability Trust 2011
Footnotes
This author gratefully acknowledges being supported by a postdoctoral grant from the AXA Research Fund.
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