A Stationary Mean-Field Model for Carbon Market Stability Reserve
Abstract
We formulate the design of a market stability reserve as a stationary mean-field singular control problem. The allowance balance follows a regime-switching diffusion, while the regulator injects or withdraws allowances through bounded-variation controls. The objective trades off the average allowance balance, its stationary dispersion, deviations from a long-run target, and intervention costs. The optimal policy is a regime-dependent band rule characterized by four reflecting thresholds. Its computation reduces to a scalar fixed-point problem combining a coupled variational inequality with the invariant distribution of the reflected process. A calibration to the EU ETS yields thresholds of the same order of magnitude as the existing Market Stability Reserve rule. Comparative statics show that volatility is the main determinant of the intervention band, whereas the frequency and duration of crisis regimes have limited effects. A simpler two-threshold policy based on average regime dynamics closely reproduces the optimal regime-dependent policy in terms of liquidity and intervention volumes.
Related
- Multiscale Nonlinear Risk Transmission in the Carbon–Fossil Energy–Clean Energy System from a Fractal-Market Perspective: Evidence from EMD–TVP-VAR and Interpretable Machine Learning
- Uniqueness and attractiveness of stationary solutions in a harvesting mean field game
- Mean-field equilibrium of heterogeneous agents under market impact
- Stability of quasi-stationary measures in high-dimensional products of mixing Markov chains
- Stationary bistable fronts on a periodic necklace graph: existence, stability and multiplicity
BibTeX
@misc{aid2026stationary,
title = {{A Stationary Mean-Field Model for Carbon Market Stability Reserve}},
author = {René Aïd and Federico Cannerozzi and Giorgio Ferrari},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33132},
eprint = {2610.33132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33132},
}
RIS
TY - UNPB
TI - A Stationary Mean-Field Model for Carbon Market Stability Reserve
AU - René Aïd
AU - Federico Cannerozzi
AU - Giorgio Ferrari
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33132
UR - https://arxiv.org/abs/2610.33132
AB - We formulate the design of a market stability reserve as a stationary mean-field singular control problem. The allowance balance follows a regime-switching diffusion, while the regulator injects or withdraws allowances through bounded-variation controls. The objective trades off the average allowance balance, its stationary dispersion, deviations from a long-run target, and intervention costs. The optimal policy is a regime-dependent band rule characterized by four reflecting thresholds. Its computation reduces to a scalar fixed-point problem combining a coupled variational inequality with the invariant distribution of the reflected process. A calibration to the EU ETS yields thresholds of the same order of magnitude as the existing Market Stability Reserve rule. Comparative statics show that volatility is the main determinant of the intervention band, whereas the frequency and duration of crisis regimes have limited effects. A simpler two-threshold policy based on average regime dynamics closely reproduces the optimal regime-dependent policy in terms of liquidity and intervention volumes.
ER -