OPTIMAL SWITCHING BETWEEN LOCKING DOWN AND OPENING THE ECONOMY BECAUSE OF AN INFECTION

We consider a two-regime switching model with the goal of minimizing the expected discounted cumulative combination of the number of infections together with an inverse economical indicator. We assume the two regime choices are between opening and locking down the economy, and the choice affects the infection rate. We also assume that the economy level also has a small influence on both the infection rate and the cumulative function being minimized. We then asymptotically find the value function and the boundaries of the stopping regions and perform a numerical calibration to draw conclusions about optimal lockdown in a pandemic.