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

2009/10/24 by Erik J. Baurdoux, Baurdoux, Erik J., Kees van Schaik +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.0910.4621

openalex publication_date 2009/10/24 · arxiv created 2010/11/15 · arxiv updated 2010/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following Baurdoux and Kyprianou [2] 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.

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