Memorandum, Department of Economics, University of Oslo 8/2015
Catastrophic risk is currently a hotly debated topic. This paper contributes to this debate by showing two results. First it shown that the value function in dynamic optimization can have an infinite derivative at some point even if the model specification has functional forms that are finite and without infinite derivatives. In the process it is shown that standard phase diagrams used in optimal control theory contain more information than generally recognized. Second we show that even if the value function has an infinite derivative at some point, it is not correct that this point should be avoided in finite time at almost any cost. The results are illustrated in a simple linear-quadratic fisheries model, but proven for a more general class of growth functions.
catastrophic risk fisheries optimal control shadow prices