Duality theory and simulation in financial engineering

This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is high-dimensional. In general, it is not possible to solve these problems exactly due to the so-called "curse of dimensionality" and as a result, approximate solution techniques are required. Approximate dynamic programming (ADP) and dual based methods have recently been proposed for constructing and evaluating good approximate solutions to these problems. In this paper we describe these ADP and dual-based methods, and the role simulation plays in each of them. Some directions for future research are also outlined.