This project addresses computational problems in financial engineering. Financial engineering deals broadly with the use of mathematical and computational tools to model the dynamics of asset prices, to value and hedge derivative securities tied to those assets, and to measure and control the risks associated with these instruments. This project will address three specific areas requiring innovative computational tools and analysis: (1) high-dimensional stochastic dynamic programming problems embedded in the valuation of American options; (2) numerical methods for jump-diffusion models based on transform analysis and asymptotics; (3) calculation of price sensitivities and related hedge parameters and risk measures using Monte Carlo methods.
The emerging field of financial engineering draws on mathematics, statistics, economics, and numerical methods to solve modeling and computational problems arising in the financial industry. The US is currently a world leader in this field, which is a source of competitive advantage in financial services. This field is also a large and growing source of employment for highly skilled individuals in the mathematical sciences. This project is part of a larger network of research and teaching activities through which the Principal Investigators interact with researchers in industry and other universities to help shape and advance the field of financial engineering. Financial engineering at Columbia spans several departments; this project will facilitate interdepartmental collaboration and help sustain a community of students and faculty from different disciplines with shared interests.
