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

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.

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Year of publication:	2015
Authors:	Hernández-Hernández, Daniel ; Yamazaki, Kazutoshi
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 125.2015, 1, p. 1-38
Publisher:	Elsevier
Subject:	Controller-and-stopper games \| Lévy processes \| Scale functions \| Continuous and smooth fit

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011077899