An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward

2023/08/04 by Mauricio Junca, Junca, Mauricio, Harold A. Moreno‐Franco +3 · 1 citation
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paper · pdf · doi:10.48550/arxiv.2308.02095

openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a singular control problem that aims to maximize the expected cumulative rewards, where the instantaneous returns depend on the state of a controlled process. The contributions of this paper are twofold. Firstly, to establish sufficient conditions for determining the optimality of the one-barrier strategy when the uncontrolled process X follows a spectrally negative Lévy process with a Lévy measure defined by a completely monotone density. Secondly, to verify the optimality of the (2n+1)-barrier strategy when X is a Brownian motion with a drift. Additionally, we provide an algorithm to compute the barrier values in the latter case.

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