Mathematical Methods for the New Commodity & Environmental Markets

新商品的数学方法

• 批准号: 1211928
• 负责人: Rene Carmona
• 金额: $ 25.98万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211928&HistoricalAwards=false
• 关键词: Mathematical; Methods; New; Commodity; &amp

CarmonaDMS-1211928 The mathematical core of the project is the study of approximate equilibriums for stochastic differential games with a large number of players. The first challenge is to initiate the probabilistic approach to the mean-field game paradigm originally advocated by Lasry and Lions. As a natural extension, the investigator develops the theoretical and practical tools needed for the optimal control of stochastic differential equations of McKean-Vlasov type, a problem that has not been studied despite the importance of its applications to the understanding of the behavior of large populations. The investigator develops a form of the Pontryagin maximum principle appropriate for these mean-field dynamics, derives the systems of mean-field Forward-Backward Stochastic Differential Equations arising from specifically crafted adjoint processes, and provides existence results for these new types of equations. The project is motivated by the dramatic societal impacts of changes in the production and prices of commodities observed in the last few years. The increase in the number of institutions investing in commodities has changed the behavior of the prices of these commodities, and their relationships among themselves and with equity prices. Moreover, the use of market mechanisms to curb emissions of greenhouse gases in the hope of controlling climate change has also affected some of these markets. The investigator focuses on new theoretical problems motivated by the energy and emissions markets, and aims at the development of tools to help risk managers, regulators, and policy makers handle the challenges of these new markets.

该项目的数学核心是研究具有大量参与者的随机微分博弈的近似均衡。第一个挑战是将概率方法引入最初由Lasry和Lions倡导的平均场博弈范式。作为自然延伸，研究者开发了McKean-Vlasov型随机微分方程的最优控制所需的理论和实践工具，尽管该问题在理解大群体行为方面具有重要的应用，但尚未被研究。研究者开发了一种适合于这些平均场动力学的庞特里亚金极大原理的形式，推导了由特别精心制作的伴随过程产生的平均场正反向随机微分方程系统，并提供了这些新类型方程的存在性结果。该项目的动机是在过去几年中观察到的商品生产和价格变化的巨大社会影响。投资大宗商品的机构数量的增加，改变了这些商品的价格行为，以及它们之间以及与股票价格的关系。此外，利用市场机制遏制温室气体排放，以期控制气候变化，也对其中一些市场产生了影响。研究者专注于能源和排放市场引发的新理论问题，并致力于开发工具来帮助风险管理者、监管者和政策制定者应对这些新市场的挑战。