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

作者：Baurdoux E J; Kyprianou A E^*; Pardo J C

来源：Stochastic Processes and Their Applications, 2011, 121(6): 1266-1289.

DOI：10.1016/j.spa.2011.02.002

• Stochastic games
• Optimal stopping
• Pasting principles
• Fluctuation theory
• Levy processes

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.

• 出版日期2011-6