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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Stochastic Games
Brownian movement
Lévy Process
Boundary value problems
Dynkin Games
Convertible Bonds
Game
Fluctuations (theory)
Free Boundary Value Problems
Compound Poisson Process
Optimal Stopping Problem
Brownian motion
Jump

Cite this

The Gapeev–Kühn stochastic game driven by a spectrally positive Lévy process. / Baurdoux, E J; Kyprianou, Andreas E; Pardo, Juan-Carlos.

In: Stochastic Processes and their Applications, Vol. 121, No. 6, 06.2011, p. 1266-1289.

Research output: Contribution to journalArticle

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