Mathematics of Emissions Markets: Design, Models, Analysis and Simulations

该研究项目的动机是环境经济学中有关利用市场机制控制温室气体排放的问题。它集中在设计和分析的上限和交易计划，并作为出发点，失败的第一阶段的加州RECLAIM计划和欧洲联盟ETS减少排放。本研究提出的一些技术问题涉及环境经济学中的新数学模型、非常一般的竞争均衡问题、大规模随机控制问题和不适定逆问题。它们都导致了优化，特别是在无限维空间，参数灵敏度分析和鲁棒性，随机数值，包括多尺度渐近近似和蒙特卡洛模拟新的数学挑战。这项工作将有助于数学在重大政策制定决策中发挥重要作用。该奖项将开展的研究旨在使政策制定者能够设计能够达到排放目标的排放市场，同时降低整体社会成本以及能源生产商在市场设计不当时可能获得的暴利。在全球变暖的经济学领域，大多数模型和大规模模拟程序都是确定性的，仍然有一个强大的阻力引入概率思维。监管不力和对所涉及风险的随机性缺乏理解，导致了先前排放市场设计中令人尴尬的公共政策失误。通过在随机分析领域内开发新的工具和策略，并展示如何将其应用于排放市场的监管，本研究的结果将有助于教育未来的科学家了解金融市场可以做什么和不能做什么，以及政策制定者和监管者了解均衡模型可以解释和证明什么。通过关注传统上一直远离从业者和政策制定者的雷达屏幕的随机模型，它将提高人们对概率建模在广泛领域中的作用的认识水平。

The research project is motivated by problems in environmental economics concerning the use of market mechanisms to control green-house gas emissions. It concentrates on the design and the analysis of cap and trade schemes, and uses as starting point, the failure of the first phases of the California RECLAIM program and the European Union ETS to reduce emissions. Some of the technical issues raised by this research involve new mathematical models in environmental economics, very general competitive equilibrium problems, large scale stochastic control problems, and ill-posed inverse problems. They all lead to new mathematical challenges in optimization, especially in infinite dimensional spaces, parameter sensitivity analysis and robustness, and stochastic numerics, including multi-scale asymptotic approximations and Monte Carlo simulations. The work will contribute to the important role that mathematics has to play in major policy making decisions.The research that will be carried out with this award is designed to empower policy makers in designing emissions markets capable to meet emissions target while at the same time, reducing the overall social costs as well as the obscene windfall profits energy producers can make when markets are poorly designed. In the area of economics of global warming, where most of the models and large scale simulation programs are deterministic, there is still a strong resistance to the introduction of probabilistic thinking. Poor regulation and a lack of understanding of the stochasticity of the risks involved, have contributed to embarrassing public policy faux pas in previous emissions market designs. By developing new tools and strategies within the realm of stochastic analysis, and by showing how they can be brought to bear on the regulation of emissions markets, the results of this research will help educate the future scientists about what financial markets can and cannot do, and policy makers and regulators about what equilibrium models can explain and justify. By focusing on stochastic models which have traditionally remained off the radar screen of practitioners and policy makers, it will raise the level of awareness for the power of probabilistic modeling in a wide range of domains.