CAREER: Financial Engineering, Incomplete Markets and Investment Under Uncertainty

Princeton University, Princeton NJ

Investigators

Abstract

This Faculty Early Career Development (CAREER) Program award provides funding for research and education in financial engineering. The focus is on the development of option pricing and valuation methodologies suitable for incomplete financial markets. Incompleteness arises in financial markets as soon as the unrealistic assumptions of a perfect market are relaxed. The classic Black and Scholes valuation is no longer applicable in such situations. The approach of utility indifference pricing, with roots in economics, has emerged recently to deal with incomplete markets, and the research aims to extend this methodology to American options with an infinite maturity. The techniques used include stochastics, partial differential equations and martingales. When incompleteness arises from non-tradability of the underlying asset, such options are useful in modeling the investment (and abandonment) decisions faced by firms. Utility indifference pricing involves choice of a suitable utility function to describe risk preferences. The second main goal of the research is to develop the concepts of time consistent utility functions. Consideration of infinite horizon American options leads to issues of valuing intermediate cashflows and complications due to the horizon. Naive limit taking results in degenerate control problems, so care must be taken to develop new approaches. This research will lead to new methods for portfolio management and links to dynamic risk measures. The results of this research will have impact in diverse areas such as corporate finance and real options. Improved corporate investment decisions arising from this research could benefit the shareholders of firms, and therefore society. Additionally, the techniques of stochastic optimal control and martingales will be of interest to researchers in mathematical finance. The finance industry will benefit from developments in utility indifference pricing techniques, as they need to cope daily with the practicalities of the incompleteness of markets when pricing derivatives.