An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909653164621824 |
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| author | Junca, Mauricio Moreno-Franco, Harold Perez, Jose Luis |
| author_facet | Junca, Mauricio Moreno-Franco, Harold Perez, Jose Luis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02095 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward Junca, Mauricio Moreno-Franco, Harold Perez, Jose Luis Optimization and Control 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. |
| title | An optimal multibarrier strategy for a singular stochastic control problem with a state-dependent reward |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2308.02095 |