Games of singular control and stopping driven by spectrally one-sided Lévy processes

Daniel Hernández-Hernández and Kazutoshi Yamazaki

Stochastic Processes and their Applications, 2015, vol. 125, issue 1, 1-38

Abstract: We study a zero-sum game where the evolution of a spectrally one-sided Lévy process is modified by a singular controller and is terminated by the stopper. The singular controller minimizes the expected values of running, controlling and terminal costs while the stopper maximizes them. Using fluctuation theory and scale functions, we derive a saddle point and the value function of the game. Numerical examples under phase-type Lévy processes are also given.

Keywords: Controller-and-stopper games; Lévy processes; Scale functions; Continuous and smooth fit (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2014.07.020

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