Optimal natural resources management under uncertainty with catastrophic risk

We examine an optimal natural resources management problem under uncertainty with catastrophic risk and investigate the optimal rate of use of a natural resource. For this purpose, we use stochastic control theory. We assume that, until a catastrophic event occurs, the stock of the natural resource is governed by a stochastic differential equation. We describe the catastrophic phenomenon as a Poisson process. From this analysis, we show the optimal rate of use of the natural resource in explicit form. Furthermore, we present comparative static results for the optimal rate of use of the natural resource.