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