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The Gapeev-Kuhn stochastic game driven by a spectrally positive Levy process

Baurdoux, Erik J. and Kyprianou, Andreas E. and Pardo, J.C. (2011) The Gapeev-Kuhn stochastic game driven by a spectrally positive Levy process. Stochastic Processes and Their Applications, 121 (6). pp. 1266-1289. ISSN 0304-4149

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Identification Number: 10.1016/j.spa.2011.02.002

Abstract

In Gapeev and Kuhn (2005) [8], the Dynkin game corresponding to perpetual convertible bonds was considered, when driven by a Brownian motion and a compound Poisson process with exponential jumps. We consider the same stochastic game but driven by a spectrally positive Levy process. We establish a complete solution to the game indicating four principle parameter regimes as well as characterizing the occurrence of continuous and smooth fit. In Gapeev and Kuhn (2005) [8], the method of proof was mainly based on solving a free boundary value problem. In this paper, we instead use fluctuation theory and an auxiliary optimal stopping problem to find a solution to the game.

Item Type: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2011 Elsevier B.V.
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 29 Jun 2011 13:19
Last Modified: 30 May 2014 14:26
URI: http://eprints.lse.ac.uk/id/eprint/36903

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