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 Program...
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| Published in | Economic theory Vol. 77; no. 1-2; pp. 169 - 196 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.02.2024
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0938-2259 1432-0479 1432-0479 |
| DOI | 10.1007/s00199-023-01493-1 |
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| 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. |
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| AbstractList | 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. 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. Keywords Controlled SIRD model * Optimal lockdown policies * Optimal control with state space constraints * Optimality conditions * Viscosity solutions Mathematics Subject Classification 49K15 * 49L20 * 49L25 JEL Classification C61 * E23 * I12 * I15 * I18 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.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. |
| Audience | Academic |
| Author | Gozzi, Fausto Zanco, Giovanni Lippi, Francesco Calvia, Alessandro |
| Author_xml | – sequence: 1 givenname: Alessandro orcidid: 0000-0003-4448-6877 surname: Calvia fullname: Calvia, Alessandro email: acalvia@luiss.it organization: Dipartimento di Economia e Finanza, LUISS University – sequence: 2 givenname: Fausto surname: Gozzi fullname: Gozzi, Fausto organization: Dipartimento di Economia e Finanza, LUISS University – sequence: 3 givenname: Francesco surname: Lippi fullname: Lippi, Francesco organization: Dipartimento di Economia e Finanza, LUISS University, Einaudi Institute for Economics and Finance – sequence: 4 givenname: Giovanni surname: Zanco fullname: Zanco, Giovanni organization: Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Università di Siena |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/37360773$$D View this record in MEDLINE/PubMed |
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| Keywords | Controlled SIRD model E23 I12 Optimal lockdown policies I15 Viscosity solutions Optimality conditions I18 49L20 Optimal control with state space constraints 49K15 49L25 C61 |
| Language | English |
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| SubjectTerms | COVID-19 Disease transmission Dynamic programming Economic theory Economic Theory/Quantitative Economics/Mathematical Methods Economics Economics and Finance Game Theory Microeconomics Optimization Prevention programs Public Finance Research Article Shelter in place Social and Behav. Sciences Value Viscosity |
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