Arbitrage Theory in Continuous Time

Arbitrage Theory in Continuous Time offers a rigorous exploration of the mathematical foundations underpinning continuous arbitrage pricing of financial derivatives. Focused on the probabilistic methods that lie at the heart of modern finance, the book introduces essential techniques such as stochastic optimal control theory and Merton's fund separation. Designed with graduate students in mind, it effectively combines the necessary mathematical background with concrete economic applications. Every novel technique is accompanied by a worked example, and the text includes a wealth of exercises to reinforce understanding. In addition, the book features comprehensive chapters on the martingale approach to optimal investment, optimal stopping theory as it applies to American options, and an insightful examination of positive interest models along with their connections to potential theory and stochastic discount factors. Published by Oxford University Press in 2019 and presented in a durable hardcover format with 512 pages, Arbitrage Theory in Continuous Time stands as an essential resource for students and practitioners seeking to master the complexities of continuous time financial markets.