Optimal Carbon Emission Control With Allowances Purchasing
Abstract
In this paper, we consider a company can simultaneously reduce its emissions and buy carbon allowances at any time. We establish an optimal control model involving two stochastic processes with two control variables, which is a singular control problem. This model can then be converted into a Hamilton-Jacobi-Bellman (HJB) equation, which is a two-dimensional variational equality with gradient barrier, so that the free boundary is a surface. We prove the existence and uniqueness of the solution. Finally, some numerical results are shown.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.08477
- arXiv:
- arXiv:2407.08477
- Bibcode:
- 2024arXiv240708477C
- Keywords:
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- Mathematics - Optimization and Control;
- Quantitative Finance - Mathematical Finance