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arXiv · 2505.23080

Optimal Periodic Double-Barrier Strategies for Spectrally Negative L\'{e}vy Processes

Kazutoshi Yamazaki·Qingyuan Zhang
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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.

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Kazutoshi Yamazaki, Qingyuan Zhang. 2025-05-29. Optimal Periodic Double-Barrier Strategies for Spectrally Negative L\'{e}vy Processes. https://arxiv.org/abs/2505.23080

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