The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy process |
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Authors: | EJ Baurdoux JC Pardo |
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Institution: | a Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE, United Kingdomb Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdomc Centro de Investigación en Matemáticas, A.C. Calle Jalisco s/n. C.P. 36240, Guanajuato, Mexico |
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Abstract: | In Gapeev and Kühn (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 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) 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. |
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Keywords: | 60J99 60G40 91B70 |
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