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

Daniel Hernandez-Hernandez; Kazutoshi Yamazaki

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arXiv · 1308.3141

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

Daniel Hernandez-Hernandez·Kazutoshi Yamazaki

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Abstract

We study a zero-sum game where the evolution of a spectrally one-sided Levy 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 Levy processes are also given.

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Daniel Hernandez-Hernandez, Kazutoshi Yamazaki. 2013-08-14. Games of singular control and stopping driven by spectrally one-sided Levy processes. https://arxiv.org/abs/1308.3141

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