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

By Erik J. Baurdoux and K. Van Schaik

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 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

Topics: QA Mathematics
Publisher: Applied Probability Trust
Year: 2011
DOI identifier: 10.1239/jap
OAI identifier: oai:eprints.lse.ac.uk:35942
Provided by: LSE Research Online

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