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

Princeton University, Princeton NJ

Investigators

Abstract

Sircar DMS-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.