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。它着重于限额和交易计划的设计和分析，并以加州回收计划和欧盟碳排放交易体系第一阶段的失败为出发点，以减少排放。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。它们都在优化，特别是在无限维空间，参数灵敏度分析和鲁棒性，以及随机数值，包括多尺度渐近逼近和蒙特卡罗模拟方面带来了新的数学挑战。这项工作将有助于数学在重大决策中发挥重要作用。与该奖项一起进行的研究旨在授权政策制定者设计能够满足排放目标的排放市场，同时降低总体社会成本，以及能源生产商在市场设计不良时可能获得的巨额暴利。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，对引入概率思维仍然存在强烈的抵制。监管不力以及对所涉及风险的随机性缺乏了解，导致了以往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开发新的工具和策略，并展示如何将它们应用于排放市场的监管，这项研究的结果将有助于教育未来的科学家，让他们了解金融市场能做什么和不能做什么，也有助于教育政策制定者和监管者，让他们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实践者和决策者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力量的认识水平。

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.