Arbitrage Theory in Continuous Time

Description

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.

About the author

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.

Table of contents

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