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

Baurdoux, Erik J. ORCID: 0000-0002-5407-0683 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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Identification Number: 10.1137/S0040585X97983778


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:
Additional Information: © 2009 Society for Industrial and Applied Mathematics
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 08 May 2009 10:59
Last Modified: 16 May 2024 00:51

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