Combined Optimal Stopping and Singular Stochastic Control

Abstract

In this article, a simple of combined singular stochastic control and optimal stopping in the jump-diffusion model is formulated and solved. We give sufficient conditions for the existence of an optimal strategy which has the same form as in continuous case given by Davis and Zervos [3] and also Karatzas et al. [5]. This result is applied to solve explicitly an example of such problem.

Keywords:

• Generalized Itô formula
• Jump-diffusions
• Local time
• Optimal harvest
• Optimal stopping
• Reflecting diffusions
• Variational inequalities

Mathematics Subject Classification:

• 49J20
• 47J20
• 49J15
• 49J40

The author wishes to express her thanks to Prof. Bernt Øksendal for valuable comments and discussions.