The global pandemic of COVID-19 has underlined the need for more coordinated responses to emergen... more The global pandemic of COVID-19 has underlined the need for more coordinated responses to emergent pathogens. These responses need to balance epidemic control in ways that concomitantly minimize hospitalizations and economic damages. We develop a hybrid economic-epidemiological modeling framework that allows us to examine the interaction between economic and health impacts over the first period of pathogen emergence when lockdown, testing, and isolation are the only means of containing the epidemic. This operational mathematical setting allows us to determine the optimal policy interventions under a variety of scenarios that might prevail in the first period of a large-scale epidemic outbreak. Combining testing with isolation emerges as a more effective policy than lockdowns, substantially reducing deaths and the number of infected hosts, at lower economic cost. If a lockdown is put in place early in the course of the epidemic, it always dominates the “laissez-faire” policy of doing nothing.
This chapter is devoted to the presentation of the \(L^2\) theory for the existence and uniquenes... more This chapter is devoted to the presentation of the \(L^2\) theory for the existence and uniqueness of mild solutions for a class of second-order infinite-dimensional HJB equations in Hilbert spaces through a perturbation approach.
In this chapter we discuss the connection between the study of infinite-dimensional stochastic op... more In this chapter we discuss the connection between the study of infinite-dimensional stochastic optimal control problems and that of second-order Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces.
A large number of recent studies consider a compartmental SIR model to study optimal control poli... more 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.
... Peter Groenewegen Marshall's Evolutionary Economics Tizi... more ... Peter Groenewegen Marshall's Evolutionary Economics Tiziano Raffaelli Money, Time and Rationality in Max Weber Austrian Connections Stephen D. Parsons ... Zouache 71 Consumption as an Investment The fear of goods from Hesiod to Adam Smith Cosimo Perrotta 72 Jean ...
In this paper, we study a first extension of the theory of mild solutions for Hamilton–Jacobi–Bel... more In this paper, we study a first extension of the theory of mild solutions for Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces to the case where the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear HJB equation. Our main goal is to establish the existence and the uniqueness of solutions to such HJB equations, which are continuously differentiable in the space variable. We also provide an application of our results to an exit-time optimal control problem, and we show that the corresponding value function is the unique solution to a semilinear HJB equation, possessing sufficient regularity to express the optimal control in feedback form. Finally, we give an illustrative example.
Stochastic Optimal Control in Infinite Dimension, 2017
We recall some basic notions of measure theory and give a short introduction to random variables ... more We recall some basic notions of measure theory and give a short introduction to random variables and the theory of the Bochner integral.
The global pandemic of COVID-19 has underlined the need for more coordinated responses to emergen... more The global pandemic of COVID-19 has underlined the need for more coordinated responses to emergent pathogens. These responses need to balance epidemic control in ways that concomitantly minimize hospitalizations and economic damages. We develop a hybrid economic-epidemiological modeling framework that allows us to examine the interaction between economic and health impacts over the first period of pathogen emergence when lockdown, testing, and isolation are the only means of containing the epidemic. This operational mathematical setting allows us to determine the optimal policy interventions under a variety of scenarios that might prevail in the first period of a large-scale epidemic outbreak. Combining testing with isolation emerges as a more effective policy than lockdowns, substantially reducing deaths and the number of infected hosts, at lower economic cost. If a lockdown is put in place early in the course of the epidemic, it always dominates the “laissez-faire” policy of doing nothing.
This chapter is devoted to the presentation of the \(L^2\) theory for the existence and uniquenes... more This chapter is devoted to the presentation of the \(L^2\) theory for the existence and uniqueness of mild solutions for a class of second-order infinite-dimensional HJB equations in Hilbert spaces through a perturbation approach.
In this chapter we discuss the connection between the study of infinite-dimensional stochastic op... more In this chapter we discuss the connection between the study of infinite-dimensional stochastic optimal control problems and that of second-order Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces.
A large number of recent studies consider a compartmental SIR model to study optimal control poli... more 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.
... Peter Groenewegen Marshall's Evolutionary Economics Tizi... more ... Peter Groenewegen Marshall's Evolutionary Economics Tiziano Raffaelli Money, Time and Rationality in Max Weber Austrian Connections Stephen D. Parsons ... Zouache 71 Consumption as an Investment The fear of goods from Hesiod to Adam Smith Cosimo Perrotta 72 Jean ...
In this paper, we study a first extension of the theory of mild solutions for Hamilton–Jacobi–Bel... more In this paper, we study a first extension of the theory of mild solutions for Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces to the case where the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear HJB equation. Our main goal is to establish the existence and the uniqueness of solutions to such HJB equations, which are continuously differentiable in the space variable. We also provide an application of our results to an exit-time optimal control problem, and we show that the corresponding value function is the unique solution to a semilinear HJB equation, possessing sufficient regularity to express the optimal control in feedback form. Finally, we give an illustrative example.
Stochastic Optimal Control in Infinite Dimension, 2017
We recall some basic notions of measure theory and give a short introduction to random variables ... more We recall some basic notions of measure theory and give a short introduction to random variables and the theory of the Bochner integral.
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Papers by Fausto Gozzi