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作者簡介
目次
商品簡介
《套利數學》包括了Models of Financial Markets on Finite Probability Spaces Utility Maximisation on Finite Probability Spaces、Bachelier and BlackScholes、The Kreps-Yan Theorem、The Dalang-Morton-Willinger Theorem A Primer in Stochastic Integration……等等。
作者簡介
作者：（瑞士）戴爾貝恩（Delbaen.F.）
目次
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 Kramkovs 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 Bacheliers 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≥ 1using 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 AssetPricing （1998）
10.1 Introduction and K~iown 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 Numraire
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
13.3 The Banach Space Generated by Maximal Contingent Claims
13.4 Some Results on the Topology of
13.5 The Value of Maximal Admissible Contingent Claims on the Set Me
13.6 The Space s under a Numdraire Change
13.7 The Closure of s 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. Yors Theorem ..
15.4.5 Proof of Theorem 15.D
15.5 Application
Part III Bibliography
References
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 Kramkovs 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 Bacheliers 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≥ 1using 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 AssetPricing （1998）
10.1 Introduction and K~iown 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 Numraire
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
13.3 The Banach Space Generated by Maximal Contingent Claims
13.4 Some Results on the Topology of
13.5 The Value of Maximal Admissible Contingent Claims on the Set Me
13.6 The Space s under a Numdraire Change
13.7 The Closure of s 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. Yors Theorem ..
15.4.5 Proof of Theorem 15.D
15.5 Application
Part III Bibliography
References
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