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

Baurdoux, Erik J. and Van Schaik, K. (2011) Further calculations for the McKean stochastic game for a spectrally negative levy process: from a point to an interval. Journal of Applied Probability, 48 (1). pp. 200-216. ISSN 0021-9002

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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.

Item Type: Article
Official URL: http://www.appliedprobability.org/content.aspx?Gro...
Additional Information: © 2011 Applied Probability Trust
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 01 Jun 2011 13:17
URL: http://eprints.lse.ac.uk/35942/

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