Geodesic
Optimal growth in a~two-sector economy facing an expected random shock
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 271-299

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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 of the economy expects the occurrence of a random shock that increases sharply abatement costs in the dirty sector. Assuming that the probability of an exogenous environmental shock is distributed according to the exponential law, we use Pontryagins maximum principle to find the optimal investment and consumption policies for the economy.
Keywords: dynamic optimization, optimal control, Pontryagin's maximum principle, endogenous growth, climate change, random shock, government policy, technological development. 
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Sergey Aseev; Konstantin Besov; Simon-Erik Ollus; Tapio Palokangas. Optimal growth in a~two-sector economy facing an expected random shock. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 2, pp. 271-299. http://geodesic.mathdoc.fr/item/TIMM_2011_17_2_a21/