Control and Financial Engineering

Abstract

The paper provides a review of the basics of financial engineering, with a few examples. We emphasize connections with control theory in a broad sense rather than with stochastic control theory in particular, and the reader is not assumed to be versed in stochastic processes. After a discussion of the main methods of financial risk management, a state-space framework for modeling financial markets is presented and used to explain crucial concepts of financial engineering such as absence of arbitrage, market completeness, hedging, and the Black-Scholes partial differential equation. Two brief case studies are presented: the construction of an indexed bond, and the hedging of long-term contracts for delivery of oil.