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

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.

To appear in Stochastic Processes and Their Applications

References in corpus (5)

• On the optimal dividend problem for a spectrally negative Lévy process
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes
• Precautionary Measures for Credit Risk Management in Jump Models
• Inventory Control for Spectrally Positive Levy Demand Processes
• The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy process