Arbitrage Theory in Continuous Time

The fourth edition of this textbook on pricing and hedging of financial derivatives, now also including dynamic equilibrium theory, continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, the book is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but the mathematical theory is also always supplemented with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Björk has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. There is also an entirely new part of the book presenting dynamic equilibrium theory. This includes several chapters on unit net supply endowments models, and the Cox–Ingersoll–Ross equilibrium factor model (including the CIR equilibrium interest rate model). Providing two full treatments of arbitrage theory—the classical delta hedging approach and the modern martingale approach—the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action.