新冠肺炎封锁的一个简单规划问题：动态规划方法。

IF 1.2 3区经济学 Q3 ECONOMICS

Economic Theory Pub Date : 2023-04-15 DOI:10.1007/s00199-023-01493-1

Alessandro Calvia, Fausto Gozzi, Francesco Lippi, Giovanni Zanco

{"title":"新冠肺炎封锁的一个简单规划问题：动态规划方法。","authors":"Alessandro Calvia, Fausto Gozzi, Francesco Lippi, Giovanni Zanco","doi":"10.1007/s00199-023-01493-1","DOIUrl":null,"url":null,"abstract":"A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.","PeriodicalId":47982,"journal":{"name":"Economic Theory","volume":" ","pages":"1-28"},"PeriodicalIF":1.2000,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10105532/pdf/","citationCount":"4","resultStr":"{\"title\":\"A simple planning problem for COVID-19 lockdown: a dynamic programming approach.\",\"authors\":\"Alessandro Calvia, Fausto Gozzi, Francesco Lippi, Giovanni Zanco\",\"doi\":\"10.1007/s00199-023-01493-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.\",\"PeriodicalId\":47982,\"journal\":{\"name\":\"Economic Theory\",\"volume\":\" \",\"pages\":\"1-28\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10105532/pdf/\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Economic Theory\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://doi.org/10.1007/s00199-023-01493-1\",\"RegionNum\":3,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economic Theory","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00199-023-01493-1","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}

引用次数: 4

摘要

最近的大量研究考虑了分区SIR模型，以研究旨在遏制新冠肺炎传播的最佳控制政策，同时最大限度地降低预防措施的经济成本。这样的问题是非凸的，并且标准结果不需要成立。我们使用动态规划方法，证明了相关优化问题的值函数的一些连续性性质。我们研究了相应的Hamilton-Jacobi-Bellman方程，并证明了值函数在粘性意义上求解该方程。最后，我们讨论了一些最优性条件。我们的论文代表了在动态规划方法中对非凸动态优化问题的完整分析的第一个贡献。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A simple planning problem for COVID-19 lockdown: a dynamic programming approach.

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Economic Theory ECONOMICS-

CiteScore

2.50

自引率

23.10%

发文量

期刊介绍： The purpose of Economic Theory is to provide an outlet for research - in all areas of economics based on rigorous theoretical reasoning, and - on specific topics in mathematics which is motivated by the analysis of economic problems. Economic Theory''s scope encompasses - but is not limited to - the following fields. - classical and modern equilibrium theory - cooperative and non-cooperative game theory - macroeconomics - social choice and welfare - uncertainty and information, intertemporal economics (including dynamical systems) - public economics - international and developmental economics - financial economics, money and banking - industrial organization Economic Theory also publishes surveys if they clearly picture the basic ideas at work in some areas, the essential technical apparatus which is used and the central questions which remain open. The development of a productive dialectic between stylized facts and abstract formulations requires that economic relevance be at the forefront. Thus, correct, and innovative, mathematical analysis is not enough; it must be motivated by - and contribute to - the understanding of substantive economic problems. Officially cited as: Econ Theory