这本《套利数学》由瑞士的Freddy Delbaen和Walter Schachemayer所著，内容是：The present book therefore is organised as follows. Part Ⅰ contains the"guided tour" which is divided into eight chapters. In Part Ⅱ we reproduce updated versions of the following papers. We havecorrected a number of typographical errors and two mathematical inaccuracies(indicated by footnotes) pointed out to us over the past years by severalcolleagues.

Part Ⅰ A Guided Tour to Arbitrage Theory

 1 The Story in a Nutshell

1.1 Arbitrage

1.2 An Easy Model of a Financial Market

1.3 Pricing by No-Arbitrage

1.4 Variations of the Example

1.5 Martingale Measures

1.6 The Fundamental Theorem of Asset Pricing

 2 Models of Financial Markets on Finite Probability Spaces

2.1 Description of the Model

2.2 No-Arbitrage and the Fundamental Theorem of Asset Pricing

2.3 Equivalence of Single-period with Multiperiod Arbitrage

2.4 Pricing by No-Arbitrage

2.5 Change of Numeraire

2.6 Kramkov's Optional Decomposition Theorem

 3 Utility Maximisation on Finite Probability Spaces

3.1 The Complete Case

3.2 The Incomplete Case

3.3 The Binomial and the Trinomial Model

 4 Bachelier and Black-Scholes

4.1 Introduction to Continuous Time Models

4.2 Models in Continuous Time

4.3 Bachelier's Model

4.4 The Black-Scholes Model

 5 The Kreps-Yan Theorem

5.1 A General Framework

5.2 No Free Lunch

 6 The Dalang-Morton-Willinger Theorem

6.1 Statement of the Theorem

6.2 The Predictable Range

6.3 The Selection Principle

6.4 The Closedness of the Cone C

6.5 Proof of the Dalang-Morton-Willinger Theorem for T=1

6.6 A Utility-based Proof of the DMW Theorem for T=1

6.7 Proof of the Dalang-Morton-Willinger Theorem for T＞1 by Induction on T

6.8 Proof of the Closedness of K in the Case T≥1

6.9 Proof of the Closedness of C in the Case T≥1 under the (NA) Condition

6.10 Proof of the Dalang-Morton-Willinger Theorem for T≥1 using the Closedness of C

6.11 Interpretation of the L∞-Bound in the DMW Theorem

 7 A Primer in Stochastic Integration

7.1 The Set-up

7.2 Introductory on Stochastic Processes

7.3 Strategies, Semi-martingales and Stochastic Integration

 8 Arbitrage Theory in Continuous Time: an Overview

8.1 Notation and Preliminaries

8.2 The Crucial Lemma

8.3 Sigma-martingales and the Non-locally Bounded Case

Part Ⅱ The Original Papers

 9 A General Version of the Fundamental Theorem of Asset Pricing (1994)

9.1 Introduction

9.2 Definitions and Preliminary Results

9.3 No Free Lunch with Vanishing Risk

9.4 Proof of the Main Theorem

9.5 The Set of Representing Measures

9.6 No Free Lunch with Bounded Risk

9.7 Simple Integrands

9.8 Appendix: Some Measure Theoretical Lemmas

 10 A Simple Counter-Example to Several Problems in the Theory of Asset Pricing (1998)

10.1 Introduction and Known Results'.

10.2 Construction of the Example

10.3 Incomplete Markets

 11 The No-Arbitrage Property under a Change of Numeraire (1995)

11.1 Introduction

11.2 Basic Theorems

11.3 Duality Relation

11.4 Hedging and Change of Numeraire

 12 The Existence of Absolutely Continuous Local Martingale Measures (1995)

12.1 Introduction

12.2 The Predictable Radon-Nikodym Derivative

12.3 The No-Arbitrage Property and Immediate Arbitrage

12.4 The Existence of an Absolutely Continuous Local Martingale Measure

 13 The Banach Space of Workable Contingent Claims in Arbitrage Theory (1997)

13.1 Introduction

13.2 Maximal Admissible Contingent Claims by Maximal Contingent Claims

13.4 Some Results on the Topology of G

13.5 The Value of Maximal Admissible Contingent Claims on the Set Me

13.6 The Space G under a Numeraire Change

13.7 The Closure of G∞ and Related Problems

 14 The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes (1998)

14.1 Introduction

14.2 Sigma-martingales

14.3 One-period Processes

14.4 The General Rd-valued Case

14.5 Duality Results and Maximal Elements

 15 A Compactness Principle for Bounded Sequences of Martingales with Applications (1999)

15.1 Introduction

15.2 Notations and Preliminaries

15.3 An Example

15.4 A Substitute of Compactness

  for Bounded Subsets of H1

  15.4.1 Proof of Theorem 15.A

  15.4.2 Proof of Theorem 15.C

  15.4.3 Proof of Theorem 15.B

  15.4.4 A proof of M. Yor's Theorem

  15.4.5 Proof of Theorem 15.D

15.5 Application

Part Ⅲ Bibliography

References