Further calculations for the McKean stochastic game for a spectrally negative Levy process: from a point to an interval

Erik J. Baurdoux; Kees van Schaik

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arXiv · 0910.4621

Further calculations for the McKean stochastic game for a spectrally negative Levy process: from a point to an interval

Erik J. Baurdoux·Kees van Schaik

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Abstract

Following Baurdoux and Kyprianou [2] we consider the McKean stochastic game, a game version of the McKean optimal stopping problem (American put), driven by a spectrally negative Levy 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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Erik J. Baurdoux, Kees van Schaik. 2010-11-15. Further calculations for the McKean stochastic game for a spectrally negative Levy process: from a point to an interval. https://arxiv.org/abs/0910.4621

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