A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-12-21 DOI:10.3934/naco.2022033

Maximilien Germain, H. Pham, X. Warin

{"title":"A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection","authors":"Maximilien Germain, H. Pham, X. Warin","doi":"10.3934/naco.2022033","DOIUrl":null,"url":null,"abstract":"We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with exact penalization and running maximum or integral cost. The method is then extended to the common noise setting. Our work extends (Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016), pp. 2568--2593) and (Bokanowski, Picarelli, and Zidani, Appl. Math. Optim. 71 (2015), pp. 125--163) to a mean-field setting. The reformulation as an unconstrained problem is particularly suitable for the numerical resolution of the problem, that is achieved from an extension of a machine learning algorithm from (Carmona, Lauri{\\`e}re, arXiv:1908.01613 to appear in Ann. Appl. Prob., 2019). A first application concerns the storage of renewable electricity in the presence of mean-field price impact and another one focuses on a mean-variance portfolio selection problem with probabilistic constraints on the wealth. We also illustrate our approach for a direct numerical resolution of the primal Markowitz continuous-time problem without relying on duality.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/naco.2022033","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 2

Abstract

We consider the control of McKean-Vlasov dynamics (or mean-field control) with probabilistic state constraints. We rely on a level-set approach which provides a representation of the constrained problem in terms of an unconstrained one with exact penalization and running maximum or integral cost. The method is then extended to the common noise setting. Our work extends (Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016), pp. 2568--2593) and (Bokanowski, Picarelli, and Zidani, Appl. Math. Optim. 71 (2015), pp. 125--163) to a mean-field setting. The reformulation as an unconstrained problem is particularly suitable for the numerical resolution of the problem, that is achieved from an extension of a machine learning algorithm from (Carmona, Lauri{\`e}re, arXiv:1908.01613 to appear in Ann. Appl. Prob., 2019). A first application concerns the storage of renewable electricity in the presence of mean-field price impact and another one focuses on a mean-variance portfolio selection problem with probabilistic constraints on the wealth. We also illustrate our approach for a direct numerical resolution of the primal Markowitz continuous-time problem without relying on duality.

查看原文本刊更多论文

状态约束McKean-Vlasov方程控制的水平集方法:在可再生能源存储和投资组合选择中的应用

我们考虑具有概率状态约束的McKean-Vlasov动力学控制(或称平均场控制)。我们依赖于一种水平集方法，它将约束问题表示为具有精确惩罚和运行最大或积分成本的无约束问题。然后将该方法推广到常见的噪声设置。我们的工作扩展了(Bokanowski, Picarelli, and Zidani, SIAM J. Control Optim. 54.5 (2016)， pp. 2568—2593)和(Bokanowski, Picarelli, and Zidani, apple .)。数学。Optim. 71 (2015)， pp. 125—163)到平均场设置。作为无约束问题的重新表述特别适合于问题的数值解决，这是通过扩展(Carmona, Lauri{\ ' e}re, arXiv:1908.01613)的机器学习算法实现的，并出现在Ann中。达成。概率。, 2019)。第一个应用涉及平均场价格影响下可再生电力的存储，另一个应用侧重于对财富有概率约束的平均方差投资组合选择问题。我们还说明了不依赖对偶的原始马科维茨连续时间问题的直接数值解决方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.