This note provides a simple proof of the necessity of the transversality condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of...

We study the importance of anticipated learning - about both environmental damages and abatement costs - in determining the level and the method of controlling greenhouse gas emissions. We also compare active learning, passive learning, and parameter uncertainty without learning. Current beliefs...

Contrary to static mean-variance analysis, very few papers have dealt with dynamic mean-variance analysis. Here, the mean-variance efficient self-financing portfolio strategy is derived for n risky assets in discrete and continuous time. In the discrete setting, the resulting portfolio is...

The objective of this paper is to study the problem of management of irrigation water. We analyse farmers' economic rules of tactical irrigation scheduling in a certain or uncertain environment under water scarcity. The optimal plans depend on uncertain weather conditions and expectations. We...