Developing a Mathematical Theory of Optimal Resource Allocation Under Climate Uncertainty for Nigerian Agriculture

Climate change presents unprecedented decision-making challenges for agricultural resource allocation in Nigeria, where temperature increases, rainfall pattern shifts, and extreme event intensification are projected to reduce crop yields by 10 to 25 percent by 2050 in multiple geopolitical zones, yet the mathematical theory for optimal allocation under this type of deep climate uncertainty remains underdeveloped in the Nigerian context. This dissertation makes original theoretical contributions to resource allocation under deep uncertainty by developing a novel robust dynamic programming framework that accommodates ambiguity about climate probability distributions, going beyond the expected utility and stochastic programming approaches that require well-specified probability models. The theoretical framework is built on the maximin expected utility axiomatics of Gilboa and Schmeidler, extended to a multi-period agricultural planning context with crop switching costs. An original proof demonstrates that the robust value function satisfies a modified Bellman equation under the ambiguity set formulation. Computational tractability is achieved through a novel reformulation as a second-order cone programme solvable by standard interior-point methods. The framework is parameterised using climate ensemble data from the CORDEX Africa project and agricultural production data across 12 states in the North West and North Central zones. Optimal robust allocation policies are shown to diversify irrigation investment and crop variety adoption 38 percent more than stochastic programming policies while incurring only 7 percent higher expected cost. Keywords: robust dynamic programming, climate uncertainty, agricultural resource allocation, ambiguity aversion, Nigeria.