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The Shepp-Shiryaev stochastic game driven by a spectrally negative Lévy process

Baurdoux, Erik J. and Kyprianou, Andreas E. (2009) The Shepp-Shiryaev stochastic game driven by a spectrally negative Lévy process. Theory of Probability and Its Applications, 53 (3). pp. 481-499. ISSN 0040-585X

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Abstract

In [15], the stochastic-game-analogue of Shepp and Shiryaev’s optimal stopping problem (cf. [23] and [24]) was considered when driven by an exponential Brownian motion. We consider the same stochastic game, which we call the Shepp–Shiryaev stochastic game, but driven by a spectrally negative L´evy process and for a wider parameter range. Unlike [15], we do not appeal predominantly to stochastic analytic methods. Principally, this is due to difficulties in writing down variational inequalities of candidate solutions on account of then having to work with nonlocal integro-differential operators. We appeal instead to a mixture of techniques including fluctuation theory, stochastic analytic methods associated with martingale characterisations and reduction of the stochastic game to an optimal stopping problem.

Item Type: Article
Official URL: http://epubs.siam.org/tvp
Additional Information: © 2009 Society for Industrial and Applied Mathematics
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Risk and Stochastics Group
Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 08 May 2009 10:59
URL: http://eprints.lse.ac.uk/23927/

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