The McKean stochastic game driven by a spectrally negative Lévy process

Erik J Baurdoux (London School of Economics)
Andreas E Kyprianou (Bath University)


We consider the stochastic-game-analogue of McKean's optimal stopping problem when the underlying source of randomness is a spectrally negative Lévy process. Compared to the solution for linear Brownian motion given in Kyprianou (2004) one finds two new phenomena. Firstly the breakdown of smooth fit and secondly the stopping domain for one of the players `thickens' from a singleton to an interval, at least in the case that there is no Gaussian component.

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Pages: 173-197

Publication Date: February 14, 2008

DOI: 10.1214/EJP.v13-484


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