The Gapeev-Kuhn stochastic game driven by a spectrally positive Levy process

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Baurdoux, E. J.²  Kyprianou, A. E.¹  Pardo, J. C.^1,3 

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] London Sch Econ, Dept Stat, London WC2A 2AE, England

[3] Ctr Invest Matemat, Guanajuato 36240, Mexico

关键词: Stochastic games;    Optimal stopping;    Pasting principles;    Fluctuation theory;    Levy processes;   

DOI  :  10.1016/j.spa.2011.02.002

来源: Elsevier

【 摘 要 】

In Gapeev and Kuhn (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 Levy 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 Kuhn (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. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.

【 授权许可】

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