The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy process
AbstractIn Gapeev and Kühn (2005) , 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 Lévy 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 Kühn (2005) , 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 6 (June)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Masahiko Egami & Tim S. T. Leung & Kazutoshi Yamazaki, 2011.
"Default Swap Games Driven by Spectrally Negative Levy Processes,"
1105.0238, arXiv.org, revised Sep 2012.
- Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
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