The Gapeev–Kühn stochastic game driven by a spectrally positive Lévy process

Reference:

Baurdoux, E. J., Kyprianou, A. E. and Pardo, J.-C., 2011. The Gapeev–Kühn stochastic game driven by a spectrally positive Lévy process. Stochastic Processes and their Applications, 121 (6), pp. 1266-1289.

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Official URL:

http://dx.doi.org/10.1016/j.spa.2011.02.002

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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