The Gapeev-Kuhn stochastic game driven by a spectrally positive Levy process
Baurdoux, E. J.
, Kyprianou, A. E. & Pardo, J.
(2011).
The Gapeev-Kuhn stochastic game driven by a spectrally positive Levy process.
Stochastic Processes and Their Applications,
121(6), 1266-1289.
https://doi.org/10.1016/j.spa.2011.02.002
, Kyprianou, A. E. & Pardo, J.
(2011).
The Gapeev-Kuhn stochastic game driven by a spectrally positive Levy process.
Stochastic Processes and Their Applications,
121(6), 1266-1289.
https://doi.org/10.1016/j.spa.2011.02.002
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.