Fall 2010: Theory of Probability I (M385C/CAM384K)

• First-day handout / course description
• Lecture notes: (files may change/be updated from time to time. Make sure to check for updates regularly. Also, make sure to clear your browser's cache before you do. Beware of typos and more serious errors - these are still very much under construction. In fact, if you spot any mistakes of any kind, I would be very grateful if you sent me an e-mail. Also, please do not try to print slides - it does not end well.)
  • Measurable Spaces   [slides]   [solutions]
  • Measures   [slides]   [solutions]
  • Lebesgue Integration   [slides]   [solutions]
  • Lebesgue Spaces and Inequalities   [slides]   [solutions]
  • Theorems of Fubini-Tonelli and Radon-Nikodym   [slides]   [solutions]
  • Basic Notions of Probability   [slides]
• Homework assignments (all problems are from lecture notes, not slides)
  • Homework assignment 1, due on Wed, Sep 8, 2010. Problems: 1.44, 1.34, 1.47
  • Homework assignment 2, due on Mon, Sep, 27, 2010. Problems: 2.34, 2.36, 2.39
  • Homework assignment 3, due on Mon, Oct 11, 2010. Problems: 3.36, 3.38, 3.39, 3.42
  • Homework assignment 4, not due. Problems: 4.27, 4.29, 5.19, 5.22, 5.23, 5.26.
  • Homework assignment 5, due on Fri, Oct 29, 2010. Problems: 5.25 (read the solution, do not submit), 6.46, 6.47, 6.48 (submit)
• Exams and Solutions:
  • The Midterm Exam is scheduled for Friday, Oct 15 Monday, Oct 18 (in class, during the regular class time). You are responsible for all the material covered by Friday, Oct 8 Monday, Oct 11.

Summer 2010: Equilibria in Incomplete Markets - Oxford-Man Institute

• Lecture slides (2 per page)

Spring 2010: Theory of Probability II (M385D/CAM384L)

• First-day handout / course description
• Lecture notes: (files may change/be updated from time to time. Make sure to check the time-stamp in the footer. Beware of typos and more serious errors - these are still very much under construction. In fact, if you spot any mistakes of any kind, I would be very grateful if you sent me an e-mail. )
  • Further discrete martingale theory [02/03] (slides [02/01])
  • Brownian motion [02/14] (slides [2/12])
    • Wiener-Fourier.nb a Mathematica notebook with some demonstrations
  • First properties of the Brownian Motion (slides [2/15])
  • Continuous martingales [3/28] (slides [3/28])
  • Quadratic variation [4/12] (slides [4/2])
  • Stochastic integration [5/03] (slides [4/30])
  • Some applications of Ito's formula 5/03] (slides [5/05])
• Homework assignments:
  • hw1
  • hw2
  • hw3
  • hw4
  • hw5
  • hw6
  • hw7 Practice problems
• Exams and Solutions:
  • Midterm .

Fall 2009: Theory of Probability I (M385C/CAM384K)

• First-day handout / course description
• Lecture notes: (files may change/be updated from time to time. Make sure to check the time-stamp in the footer. Beware of typos and more serious errors - these are still very much under construction. In fact, if you spot any mistakes of any kind, I would be very grateful if you sent me an e-mail. )
  • Measurable Spaces [09/20] (slides [08/27])
  • Measures [09/12] (slides [09/02])
  • Lebesgue integration [09/17] (slides [09/16])
  • Lebesgue spaces and inequalities [09/23] (slides [09/23])
  • Theorems of Fubini-Tonelli and Radon-Nikodym [09/28] (slides [09/28])
  • Basic Notions of Probability [10/11] (slides [10/12])
  • Weak Convergence of Probability Measures [10/22] (slides [10/19])
  • Characteristic functions [10/25] (slides [10/25])
  • WLLN and CLT [10/31] (slides [10/31])
  • Conditional Expectation [11/06] (slides [11/06])
  • Discrete Martingales [11/20] (slides [11/16])
  • Uniform Integrability and Martingales [11/17] (slides [11/18])
  The date in brackets is the last time a file has been updated. I try to keep up with typos I/you find in the lectures. Not so much for the slides.
• Homework assignments:
  • hw1
  • hw2
  • hw3
  • hw4
  • hw5
  • hw6
  • hw7
  • hw8
  • hw9
  • hw10
  • hw11
• Exams and Solutions:
  • Midterm: problems and solutions, statistics.

Spring 2009: Theory of Probability II (M385D/CAM384L)

• First-day handout / course description

Fall 2008: Introduction to Stochastic Processes (M362M)

• First-day handout

Spring 2008: Introduction to Stochastic Processes (M362M)

Fall 2007: Theory of Probability I (M385C/CAM384K)

• Course description
• First-day handout

Spring 2007: Topics in Stochastic Analysis (M393C/CAM393C)

• Course description
• Lecture notes (on discrete equilibrium theory):
  • Lecture 1
  • Lecture 2
  • Lecture 3
  • Lecture 4
  • Lecture 5
  • Lecture 6

Fall 2006: Theory of Probability I (M385C/CAM384K)

Spring 2006: Topics in Stochastic Analysis (M393C/CAM393C)

• Course description
• Lecture notes (very much under construction):
  • Introduction
  • Chapter 1 (Semimartingales)
  • Chapter 1 (problems)
  • Chapter 2 (Lévy processes)
  • Chapter 2 (problems)
  • Chapter 3 (financial markets)
  • Chapter 3 (problems)
  • Appendix A (a few facts from measure theory)
  • Appendix B (two theorems about martingales)
  • Bibliography (annotated)

Fall 2005: Matrices and Matrix Computations (M340L)

Spring 2005: Continuous-time Finance (at Carnegie Mellon University)

• A set of lecture notes (one large file)