Duality Theory and Approximate Dynamic Programming for Pricing American Options and Portfolio Optimization

This chapter describes how duality and approximate dynamic programming (ADP) methods can be used 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. ADP and dual-based methods have been proposed for constructing and evaluating good approximate solutions to these problems. In this chapter we describe these methods. Some directions for future research are also outlined.