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arXiv · 2308.02095

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

Mauricio Junca·Harold Moreno-Franco·Jose Luis Perez
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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 L\'evy process with a L\'evy 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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Mauricio Junca, Harold Moreno-Franco, Jose Luis Perez. 2023-08-04. An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward. https://doi.org/10.1007/s00245-024-10176-9

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