一类具有方向切换代价的奇异随机控制问题

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Mathematical Methods of Operations Research Pub Date : 2023-10-03 DOI:10.1007/s00186-023-00839-8

Łukasz Kruk

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引用次数: 0

摘要

摘要提出了一类新的奇异随机控制问题，在该类问题中，过程控制器不仅可以选择推力强度，其代价与其动作引起的位移成正比，而且还可以改变允许的控制方向，每次这样的切换都要付出固定的代价。详细分析了具有二次瞬时代价函数和代价方向切换的一维布朗运动在无限时间范围上的奇异控制问题，得到了一个闭合解。这个例子用来说明这里考虑的这类问题与经典的奇异随机控制之间的质的区别。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A singular stochastic control problem with direction switching cost

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A singular stochastic control problem with direction switching cost

Abstract We introduce a new class of singular stochastic control problems in which the process controller not only chooses the push intensity, at a price proportional to the displacement caused by his action, but he can also change the allowable control direction, paying a fixed cost for each such switching. Singular control of the one-dimensional Brownian motion with quadratic instantaneous cost function and costly direction switching on the infinite time horizon is analyzed in detail, leading to a closed-form solution. This example is used as an illustration of qualitative differences between the class of problems considered here and classic singular stochastic control.

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来源期刊

Mathematical Methods of Operations Research 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.