文档介绍：Steven Shreve: Stochastic Calculus and Finance
PRASAD CHALASANI SOMESH JHA
Carnegie Mellon University Carnegie Mellon University
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THIS IS A DRAFT: PLEASE DO NOT DISTRIBUTE
c Copyright; Steven E. Shreve, 1996
October 6, 1997
Contents
1 Introduction to Probability Theory 11
The Binomial Asset Pricing Model .......................... 11
Finite Probability Spaces ............................... 16
Lebesgue Measure and the Lebesgue Integral .................... 22
General Probability Spaces .............................. 30
Independence ..................................... 40
Independence of sets . . . .......................... 40
Independence of
-algebras ......................... 41
Independence of random variables ...................... 42
Correlation and independence ........................ 44
Independence and conditional expectation. . . ............... 45
Law of Large Numbers . . .......................... 46
Central Limit Theorem . . .......................... 47
2 Conditional Expectation 49
A Binomial Model for Stock Price Dynamics .................... 49
Information . ..................................... 50
Conditional Expectation ............................... 52
An example .................................. 52
Definition of Conditional Expectation .................... 53
Further discussion of Partial Averaging ................... 54
Properties of Conditional Expectation .................... 55
Examples from the Binomial Model ..................... 57
Martingales . ..................................... 58
1
2
3 Arbitrage Pricing 59
Binomial Pricing ................................... 59
General one-step APT ................................. 60
Risk-Neutral Probability Measure .......................... 61
Portfolio Process .........