Skip to main content
Article thumbnail
Location of Repository

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

By Erik J. Baurdoux, Andreas E. Kyprianou and J.C. Pardo

Abstract

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

Topics: QA Mathematics
Publisher: Elsevier
Year: 2011
DOI identifier: 10.1016/j.spa.2011.02.002
OAI identifier: oai:eprints.lse.ac.uk:36903
Provided by: LSE Research Online

Suggested articles

Citations

  1. Convexity and smoothness of scale functions and de Finetti’s control problem. doi
  2. (2007). Fluctuation theory and stochastic games for spectrally negative L´ evy processes.
  3. (2006). Introductory lectures of fluctuations of L´ evy processes with applications. doi
  4. (1999). L´ evy Processes and Infinitely Divisible Distributions. doi
  5. (2006). Optimal Stopping and Free Boundary Value Problems. Birkh¨ auser Verlag,
  6. (2008). Optimal stopping games and Nash equilibrium. Theory Probab. doi
  7. (2008). Optimal Stopping games for Markov processes. doi
  8. (2008). Optimal stopping rules. doi
  9. (2009). Smoothness of scale functions for spectrally negative L´ evy processes. doi
  10. (2005). Some remarks on the first passage of L´ evy processes, the American put and smooth pasting. doi
  11. (2004). Stochastic Integration and Differential Equations. Applications of Mathematics, Stochastic Modelling and Applied Probability. doi
  12. (2002). Stochastic Integration with Jumps. doi
  13. (2008). The McKean stochastic game driven by a spectrally negative L´ evy process. doi
  14. (1996). The Shepp–Shiryaev stochastic game driven by a spectrally negative L´ evy process. doi
  15. (2005). uhn: Perpetual convertible bonds in jump-diffusion models. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.