金融市場數學(英文版)

Preface
Preface to the Second Edition
1 Prlcing by Arbitrage
1.1 Introduction: Pricing and Hedging
1.2 Single-Period Option Pricing Models
1.3 A General Single-Period Model
1.4 A Single-Period Binomial Model
1.5 Multi-period Binomial Models
1.6 Bounds on Option Prices
2 Martingale Measures
2.1 A General Discrete-Time Market Model
2.2 Trading Strategies
2.3 Martingales and Risk-Neutral Pricing
2.4 Arbitrage Pricing: Martingale Measures
2.5 Strategies Using Contingent Claims
2.6 Example: The Binomial Model
2.7 From CRR to Blaek-Scholes
3 The First Fundamental Theorem
3.1 The Separating Hyperplane Theorem in Rn
3.2 Construction of Martingale Measures
3.3 Pathwise Description
3.4 Examples
3.5 General Discrete Models
4 Complete Markets
4.1 Completeness and Martingale Representation
4.2 Completeness for Finite Market Models
4.3 The CRR Model
4.4 The Splitting Index and Completeness
4.5 Incomplete Models: The Arbitrage Interval
4.6 Characterisation of Complete Models
5 Discrete-time American Options
5.1 Hedging American Claims
5.2 Stopping Times and Stopped Processes
5.3 Uniformly Integrable Martingales
5.4 Optimal Stopping: The Snell Envelope
5.5 Pricing and Hedging American Options
5.6 Consumption-Investment Strategies
6 Continuous-Time Stochastic Calculus
6.1 Continuous-Time Processes
6.2 Martingales
6.3 Stochastic Integrals
6.4 The It8 Calculus
6.5 Stochastic Differential Equations
6.6 Markov Property of Solutions of SDEs
7 Continuous-Time European Options
7.1 Dynamics
7.2 Girsanov’’s Theorem
7.3 Martingale Representation
7.4 Self-Financing Strategies
7.5 An Equivalent Martingale Measure
7.6 Black-Scholes Prices
7.7 Pricing in a Multifactor Model
7.8 Barrier Options
7.9 The Black-Scholes Equation
7.10 The Greeks
8 The American Put Option
8.1 Extended Trading Strategies
8.2 Analysis of American Put Options
8.3 The Perpetual Put Option
8.4 Early Exercise Premium
8.5 Relation to Free Boundary Problems
8.6 An Approximate Solution
9 Bonds and Term Structure
9.1 Market Dynamics
9.2 Future Price and Futures Contracts
9.3 Changing Numeraire
9.4 A General Option Pricing Formula
9.5 Term Structure Models
9.6 Short-rate Diffusion Models
9.7 The Heath-Jarrow-Morton Model
9.8 A Markov Chain Model
10 Consumption-Investment Strategies
10.1 Utility Functions
10.2 Admissible Strategies
10.3 Maximising Utility of Consumption
10.4 Maximisation of Terminal Utility
10.5 Consumption and Terminal Wealth
11 Measures of Risk
11.1 Value at Risk
11.2 Coherent Risk Measures
11.3 Deviation Measures
11.4 Hedging Strategies with Shortfall Risk
Bibliography
Index