Optimal Abatement Schedules for Excess Carbon Emissions Towards a Net-Zero Target

Battle Count: 89

The paper is primarily about climate policy and carbon emission management. However, it has indirect relevance to quantitative trading through: (1) the connection to optimal dividend problems in insurance risk theory, which shares mathematical structure with portfolio optimization; (2) potential applications in carbon trading markets and ESG investing; (3) the stochastic control framework (HJB equations, viscosity solutions) is transferable to trading strategy optimization. The direct applicability to trading is limited.

The theoretical framework requires advanced knowledge of stochastic control, viscosity solutions of PDEs, and Brownian motion theory. Numerical implementation involves: (1) solving a system of ODEs recursively for discrete emission rates, (2) optimizing threshold functions via one-dimensional minimization, (3) Monte Carlo simulation for validation, (4) handling the convergence from discrete to continuous control sets. The algorithm is well-specified but requires careful numerical implementation of the recursive threshold construction.

The paper provides complete mathematical derivations, explicit formulas for the HJB equation, recursive construction of the optimal threshold strategy, and specific numerical parameters (µ, σ, q, Λ, c̄, n=500). However, no code or computational scripts are provided. The numerical illustrations can be reproduced from the described algorithm, but implementation requires significant effort in solving ODEs and performing Monte Carlo simulations.