Further calculations for the McKean stochastic game for a spectrally negative Levy process: from a point to an interval

E J Baurdoux, Kees Van Schaik

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Following Baurdoux and Kyprianou (2008) we consider the McKean stochastic game, a game version of the McKean optimal stopping problem (American put), driven by a spectrally negative Levy process. We improve their characterisation of a saddle point for this game when the driving process has a Gaussian component and negative jumps. In particular, we show that the exercise region of the minimiser consists of a singleton when the penalty parameter is larger than some threshold and 'thickens' to a full interval when the penalty parameter drops below this threshold. Expressions in terms of scale functions for the general case and in terms of polynomials for a specific jump diffusion case are provided.
Original languageEnglish
Pages (from-to)200-216
Number of pages17
JournalJournal of Applied Probability
Volume48
Issue number1
DOIs
Publication statusPublished - Mar 2011

Keywords

  • optimal stopping
  • stochastic game
  • fluctuation theory
  • Levy process

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