Exogenous Hazard Rates and Precautionary Behaviour in Resource Economic Dynamics

Economic analysis of catastrophic risk is a topic that unfortunately has become more relevant since the 1960s. An important question when a vital resource stock is at risk is whether one should invest more in the stock to create a buffer against a catastrophe or allow the stock to decrease as risk makes its future value decrease. The present paper analyses exogenous catastrophic risk where the probability of catastrophe cannot be controlled. Conditions for when precautionary behaviour is optimal are given with general functional forms. The paper analyses both problems with a single catastrophe and problems with an infinite sequence of catastrophes. It is shown that most of the results pertaining to a single catastrophe carry over to the case with an infinite number of catastrophes.