Computational Methods in Financial Engineering

Columbia University, New York NY

Investigators

Abstract

PROJECT ABSTRACT: The project proposed is for the development of computational methods 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 the underlying assets, and to measure and control the risks associated with these instruments. The project proposes three areas of investigation: (1) a stochastic mesh method for solving high-dimensional stochastic dynamic programming problems embedded in certain financial engineering problems; (2) models and methods for incorporating jumps in diffusion-based models of the term structure of interest rates; (3) numerical methods for path-dependent options. Research in financial engineering contributes to the competitiveness and soundness of the U.S. financial services industry. The U.S. holds a leadership position in this important sector of the service economy; future preeminence in this industry will rely on innovation in financial services and in the technology that supports these services, including leading-edge computational methods for financial engineering and risk management. This area employs highly skilled scientists and engineers; this project will contribute, in part, to the training of skilled personnel.