Stochastic Calculus

January-February 2013

Instructor:

Giovanni Pistone

Collegio Carlo Alberto
Camerata III
Office Hours: by appointment
+39 011 670 5033
giovanni.pistone@carloalberto.org
http:// www.giannidiorestino.it

Objective of the course:

The course discusses the basics of Stochastic Calculus, from Brownian Motion to multivariate Ito's formula, and selected applications.

Contents:

1. Probability theory: conditional expectation, conditional distributions, martingales, multivariate normal distribution, divergence, Hermite polyomials. (week 1)

2. Brownian motion: as a limit of random walks, as a Gaussian process, as a martingale, as a Markov process. (week 2)

3. Ito's stochastic integral. Ito,s multiple integral. (week 3)

4. Ito's formula and applications to stochastic differential equations. (week 4)

5. Applications. (week 5)

Exam: 

Weekly homeworks will be graded and contribute 80% of the final mark. The final exam consists of a discussion of the homeworks and a (very short) paper.

Textbooks

Basic Probability: J. Jacod & Ph. E. Protter (2003)  Probability Essentials, Springer

Stochastics: Ch. 1 to 5 of S. E. Shreve (2004) Stochastic Calculus for Finance II Continuous-Time Models Springer

Course schedule: 

20 hours in 5 weeks starting Jan 9, 2013

Wed Jan 9 11-13
Wed Jan 9 14-16
Wed Jan 16 14-16
Thu Jan 17 14-16
Wed Jan 23 14-16
Thu Jan 24 14-16
Tue Jan 29 14-16
Thu Jan 31 14-16
Wed Feb 6 14-16
Thu Feb 7 14-16