The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy process (Q544519)

In [\textit{P. V. Gapeev} and \textit{C. Kühn}, Stat. Decis. 23, No. 1, 15--31 (2005; Zbl 1076.60508)], the Dynkin game corresponding to perpetual convertible bonds was considered, when driven by a Brownian motion and a compound Poisson process with exponential jumps. The authors consider the same stochastic game but driven by a spectrally positive Lévy process. They 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 [loc. cit.], the method of proof was mainly based on solving a free boundary value problem. In this paper, the authors instead use fluctuation theory and an auxiliary optimal stopping problem to find a solution to the game.