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

Baurdoux, Erik J. ORCID: 0000-0002-5407-0683 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
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	01 Jun 2011 13:17
Last Modified:	01 Oct 2024 03:37
URI:	http://eprints.lse.ac.uk/id/eprint/35942

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