奖励取决于状态的奇异随机控制问题的最佳多屏障策略

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-09-12 DOI:10.1007/s00245-024-10176-9

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

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引用次数: 0

摘要

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。

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

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

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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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.