谱正Lévy过程驱动的Gapeev-Kühn随机对策
The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy process
摘要：
Gapeev and Kühn（2005）研究了在布朗运动和带指数跳的复合泊松过程驱动下，永续可转换债券的随机对策。我们考虑相同的随机对策，但由一个谱正Lévy过程驱动。我们建立了一个完整的解决方案，游戏指示四个主要参数制度，以及表征连续和光滑的配合发生。在Gapeev和Kühn（2005）中，证明方法主要基于解决一个自由边界值问题。在本文中，我们使用波动理论和辅助最优停止问题来找到一个解决方案的游戏。
英文摘要：
In Gapeev and Kühn (2005), the stochastic 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 occurence 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
