Days (2 classes)

1. Tuesday, July 10: Conditional Probability. Probability Review. Solutions to Conditional Probability Problems. The Monte Hall Game Show and the statistical method.

2. Wednesday, July 11: The Central Limit Theorem and Stock Prices. More Probability Review.

3. Thursday, July 12: Random Variables and Transforms. Even More Probability Review.

4. Monday, July 16: Markov Mouse, Chapter 4, Introduction to Markov Chains. Supporting material on the optional Banach-Picard contraction fixed-point theorem.

5. Wednesday, July 18: More DTMC's. A credit-risk example. Paper with Professor Derman and Kunsoo Park on Markov chain models to estimate the premium from extended hedge fund lockup. Second class on reversibility, Section 4.8 of Ross.

6. Monday, July 23: trip to the post office , Chapter 5: The exponential Distribution and the Poisson Process. And SOLUTIONS to the post office problem. A Concise Summary of everything you need to know.

7. Wednesday, July 25: Chapter 6, Introduction to continuous-time Markov chains. Additional lecture notes on CTMC's .

8. Monday, July 30: MIDTERM EXAM, Chapters 1-6. 10:00am-2:00pm, Open book, open notes. Topics to Review . The exam itself.

9. Wednesday, August 1: car-buying model, stopping times, Wald's equation , Chapter 7, Renewal Theory.

10. Monday, August 6: Arbitrage, Section 10.4, and the Binomial Lattice Model.

11. Wednesday, August 8: conditional expectation, Brownian motion and martingales, Chapter 10.

12. Monday, August 13: stochastic calculus, stochastic integrals, stochastic differential equations and Ito's Lemma.

13. Wednesday, August 15: Ito's lemma, following last notes.

14. Monday, August 20: the Black-Scholes equation.

15. Wednesday, August 22: FINAL EXAM. Open book, open notes, 1:00pm.