Arbitrage Theory in Continuous Time

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Tomas Björk (Professor of Mathematical Finance, Professor of Mathematical Finance, Department of Finance, Stockholm School of Economics)

Arbitrage Theory in Continuous Time

Tomas Björk (Professor of Mathematical Finance, Professor of Mathematical Finance, Department of Finance, Stockholm School of Economics)

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English

Oxford University Press
19 December 2019

Economics; Investment & securities; Applied mathematics; Stochastics

Series: Oxford Finance Series

The fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and 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, Arbitrage Theory in Continuous Time 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 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. This edition includes an entirely new section presenting dynamic equilibrium theory, covering unit net supply endowments models and the Cox-Ingersoll-Ross equilibrium factor model. Providing two full treatments of arbitrage theory-the classical delta hedging approach and the modern martingale approach-this book is written so 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. This textbook is a natural choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in the market.

By: Tomas Björk (Professor of Mathematical Finance Professor of Mathematical Finance Department of Finance Stockholm School of Economics)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Edition: 4th Revised edition
Dimensions: Height: 241mm, Width: 162mm, Spine: 36mm
Weight: 1g
ISBN: 9780198851615
ISBN 10: 0198851618
Series: Oxford Finance Series
Pages: 592
Publication Date: 19 December 2019
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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

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.

Reviews for Arbitrage Theory in Continuous Time

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. * Short Book Reviews *