Stochastic Calculus I & II: Course Outline for Stochastic Calculus I (MAT 645)
The Binomial Asset Pricing Model, Finite Probability Spaces, Lebesgue Measure and the Lebesgue Integral,General Probability Spaces, Independence, Independence of sets, Independence of _-algebras, Independence of random variables, Correlation and independence, Independence and conditional expectation, Law of Large Numbers, Central Limit Theorem.
A Binomial Model for Stock Price Dynamics, Information, Conditional Expectation, An example. Definition of Conditional Expectation, Further discussion of Partial Averaging, Properties of Conditional Expectation, Examples from the Binomial Model, Martingales.
Binomial Pricing, Risk-Neutral Probability Measure, Portfolio Process, Self-financing Value of a Portfolio Process, Simple European Derivative Securities, The Binomial Model is Complete. Markov Processes, Different ways to write the Markov property with applications.