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

Alessandro Calvia (), Fausto Gozzi (), Francesco Lippi and Giovanni Zanco ()
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Alessandro Calvia: LUISS University
Fausto Gozzi: LUISS University
Giovanni Zanco: Università di Siena

Economic Theory, 2024, vol. 77, issue 1, No 6, 169-196

Abstract: 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.

Keywords: Controlled SIRD model; Optimal lockdown policies; Optimal control with state space constraints; Optimality conditions; Viscosity solutions; 49K15; 49L20; 49L25 (search for similar items in EconPapers)
JEL-codes: C61 E23 I12 I15 I18 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00199-023-01493-1

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