Springer - Stochastic Calculus for Finance I The Binomial Asset Pricing Model (1998).pdf

文档介绍：Steven Shreve: Stochastic Calculus and Finance
PRASAD CHALASANI SOMESH JHA
Carnegie Mellon University Carnegie Mellon University
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c Copyright; Steven E. Shreve, 1996
July 25, 1997
Contents
1 Introduction to Probability Theory 11
.......................... 11
Finite Probability Spaces ............................... 16
.................... 22
General Probability Spaces .............................. 30
..................................... 40
Independenceofsets............................. 40
Independence of  -algebras......................... 41
Independence of random variables ...................... 42
Correlationandindependence........................ 44
Independenceandconditionalexpectation.................. 45
LawofLargeNumbers............................ 46
CentralLimitTheorem............................ 47
2 Conditional Expectation 49
.................... 49
...................................... 50
............................... 52
Anexample.................................. 52
Definition of Conditional Expectation .................... 53
FurtherdiscussionofPartialAveraging................... 54
PropertiesofConditionalExpectation.................... 55
ExamplesfromtheBinomialModel..................... 57
...................................... 58
1
2
3 Arbitrage Pricing 59
................................... 59
-stepAPT................................. 60
Risk-Neutral Probability Measure .......................... 61
PortfolioProcess............................... 62
Self-financing Value of a Portfolio Process
................ 62
Simple European Derivati