Mathematical Programming Tools to Deal with Uncertainty in Climate Economics - Chang, Wonjun (ProQuest Dissertations & Theses, 2017)
How does risk and uncertainty in climate thresholds impact optimal short-run mitigation? Determining the impact of uncertain climate outcomes on near-term climate policy has long been a subject of debate in the integrated assessment community. In this dissertation I present mathematical programming tools to assess this so called "uncertainty effect'' on climate policy. I first present a minimal act-then learn stochastic control model (DICESC) based on Bayesian learning. This captures the sequential process of decision making under uncertainty based on new observational evidence. In an act-then learn setting the possibility of climate tipping in the future increases optimal abatement to delay or avoid threshold damages. While uncertainty increases the incentive for precautionary abatement, increments in mitigation and the expected value of perfect information (EVPI) may not be robust, as these can depend on higher moments of the Bayesian prior. Hazard rate distributions sharing the same mean and standard deviation may have different values of information and optimal short term mitigation policies. Humility is called for as it seems unlikely that we can determine the distribution of risk with sufficient precision. Insufficient precision in the Bayesian prior necessitates focus on the notion of ambiguity. Given multiple distributions of risk, I implement four models of ambiguity aversion and derive optimal policies for each ambiguity attitude. Results indicate a robust precautionary incentive to increase abatement under ambiguity aversion. Since effective priors are defined as a mixture of the prior set in each period, abrupt transitions between priors can impose threshold effects on policy even before tipping occurs; an ambiguity averse agent exhibits incentives to delay reaching temperature points at which the assumed Bayesian prior takes a turn for the worse. In the last chapter, I present a mixed complementarity problem (MCP) formulation of dynamic programming (DP) problems. The MCP approach replaces conventional value function iteration by the solution of a one-shot square system of equations and inequalities. Three numerical examples illustrate my approach and demonstrate that the DP-MCP algorithm can compute equilibria much faster than traditional value iteration. In addition, the MCP approach accommodates corner solutions in the optimal policy.