Optimal growth in a two-sector economy facing an expected random shock

We develop an optimal growth model of an open economy that uses both an old ("dirty" or "polluting") technology and a new ("clean") technology simultaneously. A planner costs in the dirty sector. Assuming that the probability of an exogenous environmental shock is distributed according to the exponential law, we use Pontryagin's maximum principle to find the optimal investment and consumption policies for the economy