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An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward
Applied Mathematics and Optimization. 2024. Vol. 90. Article 37.
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.
Keywords: Singular controlMultibarrier strategiesState-dependent instantaneous rewardИсключительный контрольСтратегии с несколькими барьерамиМгновенное вознаграждение, зависящее от состояния
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