An Optimal Multibarrier Strategy for a Singular Stochastic Control Problem with a State-Dependent Reward

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-12 DOI:10.1007/s00245-024-10176-9

Mauricio Junca, Harold A. Moreno-Franco, Jose-Luis Pérez

引用次数: 0

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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奖励取决于状态的奇异随机控制问题的最佳多屏障策略

我们考虑了一个奇异控制问题，其目的是最大化预期累积回报，其中瞬时回报取决于受控过程的状态。本文有两方面的贡献。首先，当非受控过程 X 遵循光谱负李维过程，且李维量度由完全单调密度定义时，本文建立了确定单壁垒策略最优性的充分条件。其次，当 X 是一个具有漂移的布朗运动时，验证（(2n+1)\）一壁垒策略的最优性。此外，我们还提供了在后一种情况下计算壁垒值的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.