Option pricing and portfolio optimization : modern methods of financial mathematics / Ralf Korn, Elke Korn.

Format:

Book

Author/Creator:

Korn, Ralf.

Contributor:

Korn, Elke, 1962-

Series:

Graduate studies in mathematics ; v. 31.

Graduate studies in mathematics ; v. 31

Standardized Title:

Optionsbewertung und Portfolio-Optimierung. English

Language:

English

German

Subjects (All):

Options (Finance)--Prices--Mathematical models.

Options (Finance).

Portfolio management--Mathematical models.

Portfolio management.

Physical Description:

xiv, 253 pages : illustrations ; 27 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2001]

Contents:

Chapter 1. The Mean-Variance Approach in a One-Period Model 1

Chapter 2. The Continuous-Time Market Model 11

2.1. Modeling the Security Prices 11

Excursion 1 Brownian Motion and Martingales 15

2.1. Continuation: Modeling the Security Prices 23

Excursion 2 The Ito Integral 26

Excursion 3 The Ito Formula 42

2.2. Trading Strategy and Wealth Process 56

2.3. Properties of the Continuous-Time Market Model 64

Excursion 4 The Martingale Representation Theorem 71

Chapter 3. Option Pricing 79

3.2. Option Pricing via the Replication Principle 83

Excursion 5 Girsanov's Theorem 93

3.2. Continuation: Option Pricing via the Replication Principle 99

3.3. Option Pricing by the Partial Differential Approach 105

Excursion 6 The Feynman-Kac Representation 111

3.4. Arbitrage Bounds for American and European Options 122

3.5. Pricing of American Options 129

3.6. Arbitrage, Equivalent Martingale Measures and Option Pricing 134

3.7. Market Numeraire and Numeraire Invariance 143

Chapter 4. Pricing of Exotic Options and Numerical Algorithms 153

4.1. Exotic Options with Explicit Pricing Formulae 155

a) Path independent options on one stock 155

b) Options on more than one underlying stock 162

c) Path dependent options 167

Excursion 7 Weak Convergence of Stochastic Processes 170

4.2. Monte-Carlo Simulation 175

4.3. Approximation via Binomial Trees 177

4.4. Trinomial Trees and Explicit Finite-Difference Methods 187

4.5. The Pathwise Binomial Approach of Rogers and Stapleton 191

Chapter 5. Optimal Portfolios 203

5.1. Introduction and Formulation of the Problem 203

5.2. The Martingale Method 206

5.3. Optimal Option Portfolios 215

Excursion 8 Stochastic Control 223

5.4. Portfolio Optimization via the Stochastic Control Method 236.

Notes:

Includes bibliographical references (pages 247-249) and index.

ISBN:

0821821237

OCLC:

45008568