Markets with transaction costs : mathematical theory

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Markets with transaction costs : mathematical theory / Yuri Kabanov, Mher Safarian

資料種別:

電子ブック

出版情報:

[Berlin ; Heidelberg] : Springer, [201-]

形態:

1 online resource (xiv, 294 p.)

シリーズ名:

Springer finance <BA37506339>

著者名:

ISBN:

9783540681212 [3540681213] (: electronic bk)

書誌ID:

TT00015881

子書誌情報

フルテキスト

所蔵情報

書誌詳細

注記:

Includes bibliographical references (p. [279]-292) and index
原資料の出版事項: Berlin ; Heidelberg : Springer , c2009

主題:

Finance--Mathematical models; Martingales (Mathematics); Transaction costs

言語:

英語

目次情報:

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 RÃ¡sonyi 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：

RÃ¡sonyi 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：

KomlÃ³ Theorem / 5.2.1：

Von WeizsÃ¤cker 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：

Explicit Formulae / 1.1.2：

Discussion / 1.1.3：

Leland-Lott Theorem / 1.2：

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