Arbitrage Theory in Continuous Time

Tomas Björk is Professor Emeritus of Mathematical Finance at the Stockholm School of Economics. He has previously worked at the Mathematics Department of the Royal Institute of Technology, also in Stockholm.Tomas Björk has been president of the Bachelier Finance Society, co-editor of Mathematical Finance, and has been on the editorial board for Finance and Stochastics and other journals. He has published numerous journal articles on mathematical finance, and in particular is known for his research on point process driven forward rate models, consistent forward rate curves, general interest rate theory, finite dimensional realisations of infinite dimensional SDEs, good deal bounds, and time inconsistent control theory.

Review from previous edition This book is one of the best of a large number of new books on mathematical and probabilistic models in finance, positioned between the books by Hull and Duffie on a mathematical scale...This is a highly reasonable book and strikes a balance between mathematical development and intuitive explanation.

• 1: Introduction I. Discrete Time Models 2: The Binomial Model 3: A More General One period Model II. Stochastic Calculus 4: Stochastic Integrals 5: Stochastic Differential Equations III. Arbitrage Theory 6: Portfolio Dynamics 7: Arbitrage Pricing 8: Completeness and Hedging 9: A Primer on Incomplete Markets 10: Parity Relations and Delta Hedging 11: The Martingale Approach to Arbitrage Theory 12: The Mathematics of the Martingale Approach 13: Black-Scholes from a Martingale Point of View 14: Multidimensional Models: Martingale Approach 15: Change of Numeraire 16: Dividends 17: Forward and Futures Contracts 18: Currency Derivatives 19: Bonds and Interest Rates 20: Short Rate Models 21: Martingale Models for the Short Rate 22: Forward Rate Models 23: LIBOR Market Models 24: Potentials and Positive Interest IV. Optimal Control and Investment Theory 25: Stochastic Optimal Control 26: Optimal Consumption and Investment 27: The Martingale Approach to Optimal Investment 28: Optimal Stopping Theory and American Options V. Incomplete Markets 29: Incomplete Markets 30: The Esscher Transform and the Minimal Martingale Measure 31: Minimizing f-divergence 32: Portfolio Optimization in Incomplete Markets 33: Utility Indifference Pricing and Other Topics 34: Good Deal Bounds VI. Dynamic Equilibrium Theory 35: Equilibrium Theory: A Simple Production Model 36: The Cox-Ingersoll-Ross Factor Model 37: The Cox-Ingersoll-Ross Interest Rate Model 38: Endowment Equilibrium: Unit Net Supply