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

SircarDMS-1211906研究人员和他的学生以及合作者研究一些金融数学和数理经济学的核心问题。他们开发了连续时间非零和博弈的分析和计算方法，这种博弈出现在寡头垄断模型中，其中少数大玩家竞争。关联的Hamilton-Jacobi-Bellman偏微分方程系统的数值解是具有挑战性的，因为一个参与者可能不会参与其中而产生退化。其目标是产生和分析正则化或平滑方案，这些方案将对数学经济学中的许多模型有用，这些模型涉及具有不同类型博弈者的差异博弈。他们还研究了投机性大宗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来研究与波动性相关的产品。随着生产从石油转向天然气，转向可再生能源，能源市场正在经历根本性变化。研究人员将这些市场分析为寡头垄断，不同燃料或技术的生产成本和供应差异很大。例如，一家石油生产商的成本相对较低，但储量枯竭，而一家太阳能生产商的成本较高，供应基本上取之不尽。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”。这是由于投机性交易员的涌入。石油或小麦等商品的价格波动，在过去十年之前主要由商品使用者的供求决定，现在更类似于股票价格更随机的波动。最后，调查员研究了波动率衍生品和杠杆交易所交易基金(ETF)等现代衍生品合约，以评估和量化它们的风险，特别是在最近的金融危机背景下。

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.