Mathematics of Energy Markets & Differential Games, Financialization of Commodities Markets, and Volatility & ETF Derivatives

能源市场数学

• 批准号: 1211906
• 负责人: K. Ronnie Sircar
• 金额: $ 23.57万
• 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=1211906&HistoricalAwards=false
• 关键词: Mathematics; Energy; Markets; & Differential

SircarDMS-1211906 The investigator and his student and collaborators study some problems central to financial mathematics and mathematical economics. They develop analytical and computational methods for continuous-time nonzero sum games that arise in models of oligopolies where a small number of large players compete. Numerical solution of the associated Hamilton-Jacobi-Bellman system of PDEs is challenging due to a degeneracy that develops because one player may not participate. The goal is to produce and analyze regularization or smoothing schemes that will be useful for many models in mathematical economics involving differential games with heterogeneous players. They also investigate the feedback mechanism from speculative commodities trading to understand market instabilities, and study volatility-related products through multiscale asymptotic analysis. Energy markets are undergoing fundamental changes as production shifts from oil to natural gas towards renewable sources. The investigator analyzes these markets as oligopolies where the production costs and supplies are very different between different fuels or technologies. For example, an oil producer has relatively low costs but exhaustible reserves, while a producer from solar technology has high costs and essentially inexhaustible supply. He also studies how commodities markets have become more "financialized" over the past decade. This is due to an influx of speculative traders. The price movements of goods such as oil or wheat, which prior to the last decade were mainly governed by supply and demand of users of the commodity, are now much more similar to the more random movements of stock prices. Finally, the investigator looks at modern derivatives contracts such as volatility derivatives and leveraged exchange traded funds, in order to assess and quantify their risks, particularly in light of the recent financial crisis.

SircarDMS-1211906 研究者和他的学生以及合作者研究金融数学和数理经济学的一些核心问题。 他们开发了连续时间非零和游戏的分析和计算方法，这些游戏出现在少数大玩家竞争的寡头垄断模型中。 相关的哈密顿-雅可比-贝尔曼系统的偏微分方程的数值解是具有挑战性的，由于退化，因为一个球员可能不参与发展。 我们的目标是产生和分析正则化或平滑方案，这将是有用的许多模型在数学经济学涉及微分游戏与异质球员。 他们还研究了投机性商品交易的反馈机制，以了解市场的不稳定性，并通过多尺度渐近分析研究波动相关的产品。 能源市场正在发生根本性变化，生产从石油转向天然气，转向可再生能源。 研究人员将这些市场分析为寡头垄断市场，不同燃料或技术之间的生产成本和供应差异很大。 例如，石油生产商的成本相对较低，但其储量是可耗尽的，而太阳能技术生产商的成本很高，而且基本上是取之不尽的。 他还研究了大宗商品市场在过去十年中如何变得更加“金融化”。 这是由于投机交易者的涌入。 石油或小麦等商品的价格变动在过去十年之前主要由商品用户的供求决定，而现在则更类似于股票价格的随机变动。 最后，研究人员着眼于现代衍生品合同，如波动性衍生品和杠杆交易所交易基金，以评估和量化其风险，特别是鉴于最近的金融危机。