Approximative Hedging / 1: |
Black-Scholes Formula Revisited / 1.1: |
Pricing by Replication / 1.1.1: |
Explicit Formulae / 1.1.2: |
Discussion / 1.1.3: |
Leland-Lott Theorem / 1.2: |
Formulation and Comments / 1.2.1: |
Proof / 1.2.2: |
Constant Coefficient: Discripancy / 1.3: |
Main Result / 1.3.1: |
Pergamenshchikov Theorem / 1.3.2: |
Rate of Convergence of the Replications Error / 1.4: |
Formulation / 1.4.1: |
Preparatory Manipulations / 1.4.2: |
Convenient Representations, Explicit Formulae, and Useful Bounds / 1.4.3: |
Tools / 1.4.4: |
Analysis of the Principal Terms: Proof of Proposition 1.4.5 / 1.4.5: |
Asymptotics of Gaussian Integrals / 1.4.6: |
Functional Limit Theorem for ? = 1/2 / 1.5: |
Limit Theorem for Semimartingale Scheme / 1.5.1: |
Problem Reformulation / 1.5.3: |
Tightness / 1.5.4: |
Limit Measure / 1.5.5: |
Identification of the Limit / 1.5.6: |
Superhedging by Buy-and-Hold / 1.6: |
Levental-Skorokhod Theorem / 1.6.1: |
Extensions for One-Side Transaction Costs / 1.6.2: |
Hedging of Vector-Valued Contingent Claims / 1.6.4: |
Arbitrage Theory for Frictionless Markets / 2: |
Models without Friction / 2.1: |
DMW Theorem / 2.1.1: |
Auxiliary Results: Measurable Subsequences and the Kreps-Yan Theorem / 2.1.2: |
Proof of the DMW Theorem / 2.1.3: |
Fast Proof of the DMW Theorem / 2.1.4: |
NA and Conditional Distributions of Price Increments / 2.1.5: |
Comment on Absolute Continuous Martingale Measures / 2.1.6: |
Complete Markets and Replicable contingent Claims / 2.1.7: |
DMW Theorem with Restricted Information / 2.1.8: |
Hedging Theorem for American-Type Options / 2.1.9: |
Stochastic Discounting Factors / 2.1.10: |
Optional Decomposition Theorem / 2.1.11: |
Martingale Measures with Bounded Densities / 2.1.13: |
Utility Maximization and convex Duality / 2.1.14: |
Discrete-Time Infinite-Horizon Model / 2.2: |
Martingale Measures in Infinite-Horizon Model / 2.2.1: |
No Free Lunch for Models with Infinite Time Horizon / 2.2.2: |
No Free Lunch with Vanishing Risk / 2.2.3: |
Example: "Retiring" Process / 2.2.4: |
The Delbaen-Schachemayer Theory in Continuous Time / 2.2.5: |
Arbitrage Theory under Transaction Costs / 3: |
Models with Transaction Costs / 3.1: |
Basic Model / 3.1.1: |
Variants / 3.1.2: |
No-arbitrage Problem: Abstract Approach / 3.1 3: |
The Grigoriev Theorem / 3.2.1: |
Counterexamples / 3.2.4: |
A Complement: The Rásonyi Theorem / 3.2.5: |
Arbitrage Opportunities of the Second Kind / 3.2.6: |
Hedging of European Options / 3.3: |
Hedging Theorem: Finite ? / 3.3.1: |
Hedging Theorem: Discrete Time, Arbitrary ? / 3.3.2: |
Hedging of American Options / 3.4: |
American Options: Finite ? / 3.4.1: |
American Options: Arbitrary ? / 3.4.2: |
Complementary Results and Comments / 3.4.3: |
Ramifications / 3.5: |
Models with Incomplete Information / 3.5.1: |
No Arbitrage Criteria: Finite ? / 3.5.2: |
No Arbitrage Criteria: Arbitrary ? / 3.5.3: |
Hedging Theorem / 3.5.4: |
Hedging Theorems: Continuous Time / 3.6: |
Introductory Comments / 3.6.1: |
Model Specification / 3.6.2: |
Hedging Theorem in Abstract Setting / 3.6.3: |
Hedging Theorem: Proof / 3.6.4: |
Rásonyi Counterexample / 3.6.5: |
Campi-Schachermayer Model / 3.6.6: |
Hedging Theorem for American Options / 3.6.7: |
When Does a Consistent Price System Exits? / 3.6.8: |
Asymptotic Arbitrage Opportunities of the Second Kind / 3.7: |
Consumption-Investment Problems / 4: |
Consumption-Investment without Friction / 4.1: |
The Merton Problem / 4.1.1: |
The HJB Equation and a Verification Theorem / 4.1.2: |
Proof of the Merton Theorem / 4.1.3: |
Robustness of the Merton Solution / 4.1.4: |
Consumption-Investment under Transaction Costs / 4.2: |
The Model / 4.2.1: |
Goal Functionals / 4.2.2: |
The Hamilton-Jacobi-Bellman Equation / 4.2.3: |
Viscosity Solution / 4.2.4: |
Ishii's Lemma / 4.2.5: |
Uniqueness of the Solution and Lyapunov Functions / 4.3: |
Uniqueness Theorem / 4.3.1: |
Existence of Lyapunov Function and Classical Supersolutions / 4.3 2: |
Supersolutions and Properties of the Bellman Function / 4.4: |
When is W Finite on K? / 4.4.1: |
Strict Local Supersolutions / 4.4.2: |
Dynamic Programming Principle / 4.5: |
The Bellman Function and the HJB Euation / 4.6: |
Properties of the Bellman Function / 4.7: |
The Subdifferential: Gneralities / 4.7.1: |
The Bellman Function of the Two-Asset Model / 4.7.2: |
Lower Bounds for the Bellman Function / 4.7.3: |
The Davis-Norman Solution / 4.8: |
Two-Asset Model: The Result / 4.8.1: |
Structure of Bellman Function / 4.8.2: |
Study of the Scalar Problem / 4.8.3: |
Skorohod Problem / 4.8.4: |
Optimal Strategy / 4.8.5: |
Precisions on the No-Transaction Region / 4.8.6: |
Liquidity Premium / 4.9: |
Non-Robustness with Respect to Transaction Costs / 4.9.1: |
First-Order Asymptotic Expansion / 4.9.2: |
Exceptional Case: ? = 1 / 4.9.3: |
Appendix / 5: |
Facts from Convex Analysis / 5.1: |
Césaro Convergence / 5.2: |
Komló Theorem / 5.2.1: |
Von Weizsäcker Theorem / 5.2.2: |
Delbaen-Schachermayer Lemma / 5.2.4: |
Facts from Probability / 5.3: |
Essential Supremum / 5.3.1: |
Generalized Martingales / 5.3.2: |
Equivalent Probabilities / 5.3.3: |
Snell Envelopes of Q-Martingales / 5.3.4: |
Measurable Selection / 5.4: |
Skorokhod Problem and SDE with Reflections / 5.5: |
Deterministic Skorokhod Problem / 5.6.1: |
Skorokhod Mapping / 5.6.2: |
Stochastic Skorokhod Problem / 5.6.3: |
Bibliographical Comments |
References |
Index |
Approximative Hedging / 1: |
Black-Scholes Formula Revisited / 1.1: |
Pricing by Replication / 1.1.1: |