Optimal Periodic Double-Barrier Strategies for Spectrally Negative L\'{e}vy Processes
Optimization and Control
2025-05-30 v1
Abstract
We study a stochastic control problem where the underlying process follows a spectrally negative L\'{e}vy process. A controller can continuously increase the process but only decrease it at independent Poisson arrival times. We show the optimality of the double-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 associated value function are written semi-explicitly using scale functions. Numerical results are also given.
Keywords
Cite
@article{arxiv.2505.23080,
title = {Optimal Periodic Double-Barrier Strategies for Spectrally Negative L\'{e}vy Processes},
author = {Kazutoshi Yamazaki and Qingyuan Zhang},
journal= {arXiv preprint arXiv:2505.23080},
year = {2025}
}