Optimality of doubly reflected Lévy processes in singular control

Erik J. Baurdoux and Kazutoshi Yamazaki

Stochastic Processes and their Applications, 2015, vol. 125, issue 7, 2727-2751

Abstract: We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Lévy process so as to minimize the total costs comprising of the running and controlling costs where the latter is proportional to the size of control. We provide a sufficient condition for the optimality of a double barrier strategy, and in particular show that it holds when the running cost function is convex. Using the fluctuation theory of doubly reflected Lévy processes, we express concisely the optimal strategy as well as the value function using the scale function. Numerical examples are provided to confirm the analytical results.

Keywords: Singular control; Doubly reflected Lévy processes; Fluctuation theory; Scale functions (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2015.01.011

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