数理金融初步 原书第3版 英文版

1 (p1): 1 Probability
1 (p1-1): 1.1 Probabilities and Events
5 (p1-2): 1.2 Conditional Probability
9 (p1-3): 1.3 Random Variables and Expected Values
14 (p1-4): 1.4 Covariance and Correlation
16 (p1-5): 1.5 Conditional Expectation
17 (p1-6): 1.6 Exercises
22 (p2): 2 Normal Random Variables
22 (p2-1): 2.1 Continuous Random Variables
22 (p2-2): 2.2 Normal Random Variables
26 (p2-3): 2.3 Properties of Normal Random Variables
29 (p2-4): 2.4 The Central Limit Theorem
31 (p2-5): 2.5 Exercises
34 (p3): 3 Brownian Motion and Geometric Brownian Motion
34 (p3-1): 3.1 Brownian Motion
35 (p3-2): 3.2 Brownian Motion as a Limit of Simpler Models
38 (p3-3): 3.3 Geometric Brownian Motion
40 (p3-3-1): 3.3.1 Geometric Brownian Motion as a Limit of Simpler Models
40 (p3-4): 3.4 The Maximum Variable
45 (p3-5): 3.5 The Cameron-Martin Theorem
46 (p3-6): 3.6 Exercises
48 (p3-7): 4 Interest Rates and Present Value Analysis
48 (p3-8): 4.1 Interest Rates
52 (p3-9): 4.2 Present Value Analysis
62 (p3-10): 4.3 Rate of Return
65 (p3-11): 4.4 Continuously Varying Interest Rates
67 (p3-12): 4.5 Exercises
73 (p4): 5 Pricing Contracts via Arbitrage
73 (p4-1): 5.1 An Example in Options Pricing
77 (p4-2): 5.2 Other Examples of Pricing via Arbitrage
86 (p4-3): 5.3 Exercises
92 (p5): 6 The Arbitrage Theorem
92 (p5-1): 6.1 The Arbitrage Theorem
96 (p5-2): 6.2 The Mulfiperiod Binomial Model
98 (p5-3): 6.3 Proof of the Arbitrage Theorem
102 (p5-4): 6.4 Exercises
106 (p6): 7 The Black-Scholes Formula
106 (p6-1): 7.1 Introduction
106 (p6-2): 7.2 The Black-Scholes Formula
110 (p6-3): 7.3 Properties of the Black-Scholes Option Cost
113 (p6-4): 7.4 The Delta Hedging Arbitrage Strategy
118 (p6-5): 7.5 Some Derivations
119 (p6-5-1): 7.5.1 The Black-Scholes Formula
121 (p6-5-2): 7.5.2 The Partial Derivatives
126 (p6-6): 7.6 European Put Options
127 (p6-7): 7.7 Exercises
131 (p7): 8 Additional Results on Options
131 (p7-1): 8.1 Introduction
131 (p7-2): 8.2 Call Options on Dividend-Paying Securities
132 (p7-2-1):…