On Stochastic Control Theory for Dynamic Carbon Emission Reduction
Summary
Addressing the reduction of Greenhouse gas emissions in the atmosphere has become crucial, given the significant implications of climate change and global warming. An effective approach to achieve emission reduction is through the implementation of a cap-and-trade system. This system involves a regulator setting a cap on the total emissions allowed and allocating allowances at a predetermined point in time to the participants. The European Union Emissions Trading System (EU ETS), introduced in 2005, serves as an example. However, the EU ETS has shown limitations in effectively compensating for economic shocks, which is necessary to let the system work accurately and to achieve the desired reduction level.
In this thesis, we investigate a novel dynamic policy of allocating allowances, aiming to provide better compensation for economic shocks. The policy is derived through a Stackelberg game, wherein a regulator, the leader, allocates allowances to set of N firms, while minimising a perceived social cost. In response to the regulator, the firms minimise their corresponding costs from abatement and trading. An important challenge is how to realistically model the cumulative Business-As-Usual (BAU) emissions of the firms, allowing for analytically tractable solutions of the policy. Two models are considered for the modelling of the BAU emissions: a Brownian motion, of which the correlation structure is generalised in this thesis, and a Geometric Brownian motion, representing the main contribution of this thesis. The SDEs of these emissions will be controlled by the abatement effort. Within both frameworks, the optimal dynamic allocations are determined through stochastic control theory and variational calculus. The proposed models are both investigated theoretically and numerically.