使用双时间尺度马尔可夫链的均值场优化切换的粘度解决方案

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2024-08-12 DOI:10.1016/j.sysconle.2024.105895

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引用次数: 0

摘要

本文考虑了粘性解概念下马尔可夫链的均值场最优切换问题。根据马尔可夫链的条件分布，建立了值函数和相应的动态编程原理。我们证明了值函数是 Wasserstein 空间上变分不等式的唯一粘性解。特别是，我们考虑了一个双时间尺度马尔可夫链，并推导出了极限系统的收敛性。作为理论结果的应用，我们解决了一个关于制度转换市场中股票交易问题的创新实例。

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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Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain

In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle are established. We prove that the value function is the unique viscosity solution of the variational inequality on Wasserstein space. In particular, we consider a two-time-scale Markov chain and derive the convergence of the limit system. As an application of theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved.

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来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.