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.

Calvia, A., Gozzi, F., Lippi, F., Zanco, G. (2024). A simple planning problem for COVID-19 lockdown: a dynamic programming approach. ECONOMIC THEORY, 77, 169-196 [10.1007/s00199-023-01493-1].

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

Zanco, G
2024-01-01

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.
2024
Calvia, A., Gozzi, F., Lippi, F., Zanco, G. (2024). A simple planning problem for COVID-19 lockdown: a dynamic programming approach. ECONOMIC THEORY, 77, 169-196 [10.1007/s00199-023-01493-1].
File in questo prodotto:
File Dimensione Formato  
s00199-023-01493-1.pdf

accesso aperto

Tipologia: PDF editoriale
Licenza: Creative commons
Dimensione 475.24 kB
Formato Adobe PDF
475.24 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1233874