Refraction strategies in stochastic control: optimality for a general L\'evy process model
- Resource Type
- Working Paper
- Authors
- Noba, Kei; Pérez, José Luis; Yamazaki, Kazutoshi
- Source
- Subject
- Mathematics - Probability
Mathematics - Optimization and Control
60G51, 93E20, 90B05
- Language
We revisit an absolutely-continuous version of the stochastic control problem driven by a L\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex. We show the optimality of a refraction strategy, which adjusts the drift of the state process at a constant rate whenever it surpasses a certain threshold. The optimality holds for a general L\'evy process, generalizing the spectrally negative case presented in Hern\'andez-Hern\'andez et al.(2016).
Comment: 24 pages