The classical DICE model is a widely accepted integrated assessment model for the joint modeling of economic and climate systems, where all model state variables evolve over time deterministically. We reformulate and solve the DICE model as an optimal control dynamic programming problem with six state variables (related to the carbon concentration, temperature, and economic capital) evolving over time deterministically and affected by two controls (carbon emission mitigation rate and consumption). We then extend the model by adding a discrete stochastic shock variable to model the economy in the stressed and normal regimes as a jump process caused by events, such as the COVID-19 pandemic. These shocks reduce the world gross output leading to a reduction in both the world net output and carbon emission. The extended model is solved under several scenarios as an optimal stochastic control problem, assuming that the shock events occur randomly on average once every 100 years and last for 5 years. The results show that, if the world gross output recovers in full after each event, the impact of the COVID-19 events on the temperature and carbon concentration will be immaterial even in the case of a conservative 10% drop in the annual gross output over a 5-year period. The impact becomes noticeable, although still extremely small (long-term temperature drops by 0.1∘C), in a presence of persistent shocks of a 5% output drop propagating to the subsequent time periods through the recursively reduced productivity. If the deterministic DICE model policy is applied in a presence of stochastic shocks (i.e., when this policy is suboptimal), then the drop in temperature is larger (approximately 0.25∘C), that is, the lower economic activities owing to shocks imply that more ambitious mitigation targets are now feasible at lower costs.
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