Refraction strategies in stochastic control: optimality for a general L\'evy process model

Kei Noba; José Luis Pérez; Kazutoshi Yamazaki

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arXiv · 2308.08183

Refraction strategies in stochastic control: optimality for a general L\'evy process model

Kei Noba·José Luis Pérez·Kazutoshi Yamazaki

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Abstract

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).

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Kei Noba, José Luis Pérez, Kazutoshi Yamazaki. 2023-08-16. Refraction strategies in stochastic control: optimality for a general L\'evy process model. https://arxiv.org/abs/2308.08183

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