Journal of Applied Probability
- J. Appl. Probab.
- Volume 48, Number 1 (2011), 200-216.
Further calculations for the McKean stochastic game for a spectrally negative é process: from a point to an interval
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.
J. Appl. Probab., Volume 48, Number 1 (2011), 200-216.
First available in Project Euclid: 15 March 2011
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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