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2008 The McKean stochastic game driven by a spectrally negative Lévy process
Erik Baurdoux, Andreas Kyprianou
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Electron. J. Probab. 13: 173-197 (2008). DOI: 10.1214/EJP.v13-484


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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Erik Baurdoux. Andreas Kyprianou. "The McKean stochastic game driven by a spectrally negative Lévy process." Electron. J. Probab. 13 173 - 197, 2008.


Accepted: 14 February 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1190.60084
MathSciNet: MR2386731
Digital Object Identifier: 10.1214/EJP.v13-484

Primary: 60J99
Secondary: 60G40 , 91B70

Keywords: fluctuation theory , L'evy processes , Optimal stopping , pasting principles , Stochastic games

Vol.13 • 2008
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