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

E.J. Baurdoux, A.E. Kyprianou and J.C. Pardo

Stochastic Processes and their Applications, 2011, vol. 121, issue 6, 1266-1289

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.

Keywords: Stochastic; games; Optimal; stopping; Pasting; principles; Fluctuation; theory; Levy; processes (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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