An explicit optimal intervention policy for a deterministic epidemic model

2007 ◽  
Vol 29 (6) ◽  
pp. 413-428 ◽  
Author(s):  
Alexei B. Piunovskiy ◽  
Damian Clancy
Keyword(s):  
Epidemic Model ◽  
Optimal Intervention ◽  
Intervention Policy

scholarly journals A Theory of Foreign Exchange Interventions

2021 ◽  
Author(s):  
Sebastián Fanelli ◽  
Ludwig Straub
Keyword(s):  
Exchange Rate ◽  
Central Bank ◽  
Interest Rates ◽  
Open Economy ◽  
Small Open Economy ◽  
Bond Markets ◽  
Pecuniary Externality ◽  
Optimal Intervention ◽  
The Exchange Rate ◽  
Intervention Policy

Abstract We study a real small open economy with two key ingredients (1) partial segmentation of home and foreign bond markets and (2) a pecuniary externality that makes the real exchange rate excessively volatile in response to capital flows. Partial segmentation implies that, by intervening in the bond markets, the central bank can affect the exchange rate and the spread between home- and foreign-bond yields. Such interventions allow the central bank to address the pecuniary externality, but they are also costly, as foreigners make carry trade profits. We analytically characterize the optimal intervention policy that solves this trade-off: (1) the optimal policy leans against the wind, stabilizing the exchange rate; (2) it involves smooth spreads but allows exchange rates to jump; (3) it partly relies on “forward guidance,” with non-zero interventions even after the shock has subsided; (4) it requires credibility, in that central banks do not intervene without commitment. Finally, we shed light on the global consequences of widespread interventions, using a multi-country extension of our model. We find that, left to themselves, countries over-accumulate reserves, reducing welfare and leading to inefficiently low world interest rates.

scholarly journals Optimal, near-optimal, and robust epidemic control

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Dylan H. Morris ◽  
Fernando W. Rossine ◽  
Joshua B. Plotkin ◽  
Simon A. Levin
Keyword(s):  
Robust Control ◽  
Disease Control ◽  
Epidemic Model ◽  
Optimal Strategy ◽  
Policy Design ◽  
Optimal Strategies ◽  
Economic Costs ◽  
Short Period ◽  
Intervention Policy ◽  
Pharmaceutical Interventions

AbstractIn the absence of drugs and vaccines, policymakers use non-pharmaceutical interventions such as social distancing to decrease rates of disease-causing contact, with the aim of reducing or delaying the epidemic peak. These measures carry social and economic costs, so societies may be unable to maintain them for more than a short period of time. Intervention policy design often relies on numerical simulations of epidemic models, but comparing policies and assessing their robustness demands clear principles that apply across strategies. Here we derive the theoretically optimal strategy for using a time-limited intervention to reduce the peak prevalence of a novel disease in the classic Susceptible-Infectious-Recovered epidemic model. We show that broad classes of easier-to-implement strategies can perform nearly as well as the theoretically optimal strategy. But neither the optimal strategy nor any of these near-optimal strategies is robust to implementation error: small errors in timing the intervention produce large increases in peak prevalence. Our results reveal fundamental principles of non-pharmaceutical disease control and expose their potential fragility. For robust control, an intervention must be strong, early, and ideally sustained.

scholarly journals Prediction and prevention of disproportionally dominant agents in complex networks

2020 ◽  
Vol 117 (44) ◽  
pp. 27090-27095
Author(s):  
Sandro Claudio Lera ◽  
Alex Pentland ◽  
Didier Sornette
Keyword(s):  
Complex Networks ◽  
Critical Mass ◽  
Stable State ◽  
Warning System ◽  
Interacting Agents ◽  
Optimal Intervention ◽  
Prediction And Prevention ◽  
The Common ◽  
Intervention Policy ◽  
Winner Takes All

We develop an early warning system and subsequent optimal intervention policy to avoid the formation of disproportional dominance (“winner takes all,” WTA) in growing complex networks. This is modeled as a system of interacting agents, whereby the rate at which an agent establishes connections to others is proportional to its already existing number of connections and its intrinsic fitness. We derive an exact four-dimensional phase diagram that separates the growing system into two regimes: one where the “fit get richer” and one where, eventually, the WTA. By calibrating the system’s parameters with maximum likelihood, its distance from the unfavorable WTA regime can be monitored in real time. This is demonstrated by applying the theory to the eToro social trading platform where users mimic each other’s trades. If the system state is within or close to the WTA regime, we show how to efficiently control the system back into a more stable state along a geodesic path in the space of fitness distributions. It turns out that the common measure of penalizing the most dominant agents does not solve sustainably the problem of drastic inequity. Instead, interventions that first create a critical mass of high-fitness individuals followed by pushing the relatively low-fitness individuals upward is the best way to avoid swelling inequity and escalating fragility.

scholarly journals Mathematical and numerical analyses of a stochastic impulse control model with imperfect interventions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hidekazu Yoshioka ◽  
Yuta Yaegashi
Keyword(s):  
Impulse Control ◽  
Bird Population ◽  
Optimal Intervention ◽  
Stochastic Impulse Control ◽  
Quasi Variational Inequality ◽  
Non Local ◽  
Intervention Policy ◽  
Hamilton Jacobi Bellman ◽  
The Many ◽  
The Value Function

AbstractA stochastic impulse control problem with imperfect controllability of interventions is formulated with an emphasis on applications to ecological and environmental management problems. The imperfectness comes from uncertainties with respect to the magnitude of interventions. Our model is based on a dynamic programming formalism to impulsively control a 1-D diffusion process of a geometric Brownian type. The imperfectness leads to a non-local operator different from the many conventional ones, and evokes a slightly different optimal intervention policy. We give viscosity characterizations of the Hamilton–Jacobi–Bellman Quasi-Variational Inequality (HJBQVI) governing the value function focusing on its numerical computation. Uniqueness and verification results of the HJBQVI are presented and a candidate exact solution is constructed. The HJBQVI is solved with the two different numerical methods, an ordinary differential equation (ODE) based method and a finite difference scheme, demonstrating their consistency. Furthermore, the resulting controlled dynamics are extensively analyzed focusing on a bird population management case from a statistical standpoint.

Wait-and-See or Step in? Dynamics of Interventions

2021 ◽  
Vol 13 (1) ◽  
pp. 399-425
Author(s):  
Dana Foarta ◽  
Takuo Sugaya
Keyword(s):  
Optimal Policy ◽  
Relational Contract ◽  
Optimal Intervention ◽  
Wait And See ◽  
Intervention Policy ◽  
Observable Effort ◽  
Threshold Rule

We study the optimal intervention policy to stop projects in a relational contract between a principal and a policymaker. The policymaker is privately informed about his ability and privately chooses how much effort to exert. Before a project is completed, the principal receives a signal about its outcome and can intervene to stop it. Intervention may prevent a bad outcome, but no intervention leads to better learning about the policymaker’s ability. In the benchmarks with observable effort or observable ability, optimal intervention follows a threshold rule. With unobservable effort and ability, the optimal policy switches between intervention and no intervention. (JEL D78, D82, D86)

scholarly journals Capital Flows and Foreign Exchange Intervention

2019 ◽  
Vol 11 (2) ◽  
pp. 127-170 ◽  
Author(s):  
Paolo Cavallino
Keyword(s):  
Financial Markets ◽  
Foreign Exchange ◽  
Open Economy ◽  
Capital Flows ◽  
Small Open Economy ◽  
Optimal Size ◽  
Economy Model ◽  
Foreign Exchange Intervention ◽  
Optimal Intervention ◽  
Intervention Policy

I consider a small open economy model where international financial markets are imperfect and the exchange rate is determined by capital flows. I use this framework to study the effects of portfolio flow shocks, derive the optimal foreign exchange intervention policy, and characterize its interaction with monetary policy. I derive the optimal intervention rule in closed form as a function of three implicit targets. Finally, using Swiss data, I estimate the model to quantify the inefficiencies generated by capital flow shocks and the optimal size of the intervention. (JEL E44, E52, E63, F31, F32, F33, F41)

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