MS&E 322 |
Stochastic Calculus and Control |
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Course
Description
This
course introduces and develops the basic concepts of stochastic calculus and
control, with an emphasis on a wide variety of applications settings including
finance, economics, queueing theory, risk theory and engineering in general.
The topics covered include Brownian motion, construction of the Ito
integral, the existence and uniqueness of solutions of stochastic differential
equations (SDEs), diffusion approximations, numerical solutions of SDEs,
controlled diffusions and the Hamilton-Jacobi-Bellman equation, and statistical
inference and parameter estimation for SDEs. A major theme will be to point out
the analogies between the more familiar theory of Markov chains and the
corresponding concepts in the SDE setting.
|
Instructor |
TA |
Lecture:
Time: Mon Wed Fri 02:15 PM - 03:30 PM See tentative class schedule here Last Updated: Jan 23 8:30pm, 2008.
Location: Redwood Hall G19
Office Hour:
TA: Tue 11:00am - 12:00pm Thur 4:00pm - 5:00pm
Review Sessions
Session 1:
Topic:
1. Basics about Conditional Expectation:
Definition, property, and examples.
2. Convergence of Random Variables:
Convergence in probability, almost sure convergence, weak
convergence, L^p convergence. Their relationship and illustrations.
Location: Terman 302
Time: Jan 24(Thur) 7:30pm-8:45pm, 2008.
Session 2:
Topic:
1) Optional Sampling: more examples and applications.
2) Change of Measure under the Markov Chain setting.
Location: Terman 498
Time: Feb 14(Thur) 7:00pm-8:15pm, 2008.
Session 3:
Topic:
More Examples on Stochastic Control.
Merton's problem,
infinite time horizon and finite time horizon case.
Location: Terman 498
Time: March 6(Thur) 7:30pm-8:45pm, 2008.
Grading
50% assignments and 50% final exam.
Final Exam
The voice of the people has been heard! Apparently, there is a majority
sentiment in terms of a 48 hour take-home exam. The take-home will be available
to be picked up from Wei Wu at 4 PM on each of the following days: Friday, March
14; Saturday, March 15; Sunday, March 16; Monday, March 17; Tuesday, March 18.
The exam must be returned within 48 hours of pick-up to Wei Wu. As with any
other exam at Stanford, the honor code applies to this exam. No collaboration of
any kind is permitted.
Homework Policy
A
homework will have a score reduced by 10% for each day of lateness, and will not
be accepted on or after the fourth day of the due date (a solution will then be
posted). For example, a solution to the first problem set will be posted on Feb
5th(Tue) and no answers will be accepted afterward. Counting of lateness starts
at the exact due time. Please communicate with the instructor or TA beforehand
in circumstances such as illness or family emergency.
The Stanford Honor Code will apply to all assignments, both in and out of class.
Copying homework from another student (past or present) is forbidden. However,
collaboration is encouraged, provided each student documents on each assignment
with whom he/she worked.
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