Year: 2026
Type: article
Abstract: We study a stochastic control problem where the underlying process follows a spectrally negative Lévy process. A controller can continuously increase the process but only decrease it at independent Poisson arrival times. We show the optimality of the periodic–classical barrier strategy, which increases the process whenever it would fall below some lower barrier and decreases it whenever it is observed above a higher barrier. An optimal strategy and the value function are written semi-explicitly using scale functions. Numerical results are also given.
Source: Journal of Applied Probability
Authors: Kazutoshi Yamazaki, Qingyuan Zhang
Institution: The University of Queensland
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7143753680