Optimal portfolio and consumption decisions for a “small investor” on a finite horizon
SIAM Journal on Control and Optimization
Martingale and duality methods for utility maximization in a incomplete market
SIAM Journal on Control and Optimization
Neuro-Dynamic Programming
Pricing American Options: A Duality Approach
Operations Research
Simulation in financial engineering: simulation in financial engineering
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Regression methods for pricing complex American-style options
IEEE Transactions on Neural Networks
Finite-Time Bounds for Fitted Value Iteration
The Journal of Machine Learning Research
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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.