Stochastic Optimization Problems in Finance

Princeton University, Princeton NJ

Investigators

Abstract

This project will study a number of risk management problems in finance requiring efficient computation of optimal trading decisions that are designed to account for various "frictions" found in modern markets. Some examples of common frictions investigated here are: uncertain volatility, influence of competition for resources, and trading restrictions. The results will be implemented as software that can be downloaded, tested and implemented by interested parties, which may range from large trading institutions to individuals with pension funds. The spectacular growth in the size of the derivatives market over the last twenty-five years (currently it has a turnover of trillions of dollars in the US), plus recent infamous (and equally spectacular) risk (mis)management disasters, such as the Barings, Orange County and Long Term Capital Management fiascos, have created an urgent need for smart mathematical and computational models to quantify the respective risks and rewards of such investments. This project aims to build on the methodology introduced by Black, Scholes and Merton, to take into account the fluctuating nature of market volatility and other frictions. The main mathematical tools are in the realm of stochastic control and asymptotic analysis.