Infinite horizon impulse control problem with continuous costs, numerical solutions

Abstract

This paper studies an infinite horizon impulse control problem where the costs are given by a diffusion process. The properties of the Snell envelope reduce this problem to the existence of a pair of continuous processes; this allows to establish an optimal impulse control solution. Finally, stability estimates and simulation results are provided.

Keywords:

• Impulse control
• infinite horizon
• reflected backward SDEs
• double barrier
• resolution by numerical schemes

Acknowledgements

The authors would like to thank the referee for his constructive comments and suggestions to improve the quality of our work. Grateful thanks to Professors H.Ouerdiane, N. Touzi and all the organizers of International Conference on Stochastic Analysis and Applications. A special thanks goes to Professor Monique Jeanblanc for her careful reading of this work.

Notes

No potential conflict of interest was reported by the authors.