An Optimal Control and Options Theory Approach to Forecasting and Managing Sustainable Systems

Sustainable management of the natural systems is essential in the presence of anthropogenic and natural disasters. Fisher information based measure and hypothesis have been proposed to quantify the sustainability of natural systems, which are used in this work to formulate management objectives. Since uncertainty is omnipresent in natural systems, its consideration is important. Real options theory deals extensively with the representation and forecasting of uncertainty. The options theory, with the Ito mean reverting process, is used to represent uncertainty, and optimal control theory is used to derive time dependent decisions. The idea is implemented on a three species predator-prey model. The results highlight the effect of uncertainty on system dynamics and decisions. When the decisions are viewed as options available to be exercised, the importance of options theory and control theory in sustainability is evident.