tailieunhanh - Steven Shreve: Stochastic Calculus and Finance

The binomial asset pricing model provides a powerful tool to understand arbitrage pricing theory and probability theory. In this course, we shall use it for both these purposes. | Steven Shreve: Stochastic Calculus and Finance PRASAD CHALASANI SOMESH JHA Carnegie Mellon University Carnegie Mellon University chal@ sjha@ THIS IS A DRAFT: PLEASE DO NOT DISTRIBUTE 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 . 60 Risk-Neutral Probability Measure 61 PortfolioProcess. 62 Self-financing Value of a Portfolio Process 62 Simple European Derivative Securities .