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


Reference:

Baurdoux, E. 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.

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Official URL:

http://dx.doi.org/10.1239/jap/1300198145

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.

Details

Item Type Articles
CreatorsBaurdoux, E. J.and Van Schaik, K.
DOI10.1239/jap/1300198145
Uncontrolled Keywordsoptimal stopping, stochastic game, fluctuation theory, levy process
DepartmentsFaculty of Science > Mathematical Sciences
RefereedNo
StatusPublished
ID Code23632

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