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.
Publié le : 2011-03-15
Classification:
Stochastic game,
optimal stopping,
é process,
fluctuation theory,
60G40,
91A15
@article{1300198145,
author = {Baurdoux, E. J. and Van Schaik, K.},
title = {Further calculations for the McKean stochastic game for a spectrally negative \'e process: from a point to an interval},
journal = {J. Appl. Probab.},
volume = {48},
number = {1},
year = {2011},
pages = { 200-216},
language = {en},
url = {http://dml.mathdoc.fr/item/1300198145}
}
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., Tome 48 (2011) no. 1, pp. 200-216. http://gdmltest.u-ga.fr/item/1300198145/