On singular control for Lévy processes

Abstract

We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality of a barrier strategy when driven by the Brownian motion or Lévy processes with one-side jumps. Under the assumption that the running cost function is convex, we show the optimality of a barrier strategy for a general class of Lévy processes.

33 pages

References in corpus (3)

• 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
• On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models

Cited by in corpus (1)

• On the optimality of the refraction--reflection strategy for Lévy processes