COURSE COVERAGE
Date  Coverage  Homework 

Precourse review  [review handout]  
Jan. 5  Binomial model. Probability, sigmafields, random variables,
expectation.

[problem set one] 
Jan. 12  Review of expectations, joint distributions, independence. Moment generating functions and characteristic functions. Conditional expectation and change of measure.  [problem set two] 
Jan. 19  Taking limits of random variables, exchanging limits. Stochastic processes, martingales, Markov chains.  [problem set three] 
Jan. 26  The original martingale (double til you win strategy)! Stochastic processes in continuous time: Poisson process, Brownian motion, martingales, and Markov property. ChapmanKolmogorov equations. Properties of Browian motion, including quadratic and total variation.  [problem set four] 
Feb. 2  Defining the Ito integral and Ito's lemma. Important properties of the Ito integral, including links with martingales. [pics]  [problem set five] 
Feb. 9  TEST ONE  
Feb. 16  READING WEEK  
Feb. 23  Ito process and chain rule version of Ito's lemma.  [problem set six] 
March 2  Diffusions, SDEs and weak/strong solutions. Financial applications: derivation of the BlackScholesMerton PDE.  [problem set seven] 
March 23  First and second fundamental theorems of asset pricing, CMG.  [problem set eight] 
March 30  TEST 2  
April 6 
Riskneutral pricing, martingale representation theorem, FeynmanKac.
Additional assigned readings (from text, unless stated otherwise):

[problem set nine] 