Optimal Carbon Emission Control With Allowances Purchasing

TL;DR

This paper develops an optimal control model for a company's carbon emission reduction and allowance purchasing, formulating it as a singular control problem with a complex HJB equation, and provides theoretical and numerical solutions.

Contribution

It introduces a novel singular control framework for joint emission reduction and allowance trading, with proof of solution existence and uniqueness.

Findings

Existence and uniqueness of the solution to the HJB equation are established.

Numerical results demonstrate the model's practical applicability.

The free boundary in the control problem is characterized as a surface.

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.