Journal of Applied Probability

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

E. J. Baurdoux and K. Van Schaik

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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 Lévy 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.

Article information

Source
J. Appl. Probab., Volume 48, Number 1 (2011), 200-216.

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1300198145

Digital Object Identifier
doi:10.1239/jap/1300198145

Mathematical Reviews number (MathSciNet)
MR2809896

Zentralblatt MATH identifier
1213.60079

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 91A15: Stochastic games

Keywords
Stochastic game optimal stopping é process fluctuation theory

Citation

Baurdoux, E. J.; Van Schaik, K. Further calculations for the McKean stochastic game for a spectrally negative é process: from a point to an interval. J. Appl. Probab. 48 (2011), no. 1, 200--216. doi:10.1239/jap/1300198145. https://projecteuclid.org/euclid.jap/1300198145


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