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

E J Baurdoux, Andreas E Kyprianou, Juan-Carlos Pardo

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1266-1289
Number of pages24
JournalStochastic Processes and their Applications
Volume121
Issue number6
DOIs
Publication statusPublished - Jun 2011

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