Optimal Carbon Emission Control With Allowances Purchasing
Optimization and Control
2024-07-12 v1 Mathematical Finance
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.
Cite
@article{arxiv.2407.08477,
title = {Optimal Carbon Emission Control With Allowances Purchasing},
author = {Xinfu Chen and Yuchao Dong and Wenlin Huang and Jin Liang},
journal= {arXiv preprint arXiv:2407.08477},
year = {2024}
}