Course description
A rapid practical introduction to stochastic calculus intended for the Mathemcaics in Finance program. Brownian motion and Ito calculus as modelign tools for random processes. The relationship between diffusion processes and partial differential equations. Strategies for random processes. See the Course Outline for specifics
Prerequisites:
A good background in probability that includes probability density functions for multi-component random variables and the multi-dimensional central limit theorem, conditional and marginal probability density in multi-dimensions using multi-variate calculus. Linear algebra including the eigenvalue probelm for symmetric matrices and quadratic forms. The ability to do scientiic computing in Python 3, including Numpy, Scipy, and Pylab.
Assignments and work flow
This COVID impacted class will be mostly remote with some in person class time depending on student interest. The following learning and workflow schedule follows math department recommendations for graduate courses this fall.
- There will be regular weekly classes on zoom from 7:10 to 9 pm each Monday.
- There will be lecture notes posted before each class Try to look at the notes before class.
- There will be a homework assignment for each class with results to be uploaded before the start of the next class.
- There will be a two hour final exam duing finals week.
Web sites:
There are two web sites for the class, a public site (this one) and an NYU Classes site for the class. Educational materials and assigmnemts will be posted on the public site. The homework upload mechanism is on the NYU Classes site. The Classes site also will have a communication forum and access to your entries in the gradebook.
Assignments, exams, grading:
The final course grade will be determined by a weighted sum of scores for assignments (60%), and the final exam (40%). I try to use the gradea A, A-, B+ and B, with lower grades only for people who "earn" them by failing to do much of the assigned work. Students who make a good faith effort should not expect a grade below B. Please contact me immediately if the material or the assignments are unmanageable, particularly if you are weak in some of the prerequisites.
Communication:
Please use the Forum page of the NYU Classes
site for this course for all content related communication,
including questions about assignments, lectures, or notes.
Feel free to contact the instructor directly about
other issues such as appointments, missed classes,
late assignments, grading issues, etc.
The instructor and TA will check the message board frequently.
Look there for important course announcements, in particular
Academic integrity
Acedemic integrity should be a mater of personal ethics. The experience of doing the assignments will prepare you for a technical interview in a way that handing in the work of another student will not. Please review the academic integrity policies of the math department and the Graduate School of Arts and Sciences. The policies for this course are
- Students are encouraged to cooperate with each other in learning the material and figuring out how to do the assignments.
- Students must create all code and assignment writeups individually. Code sharing is not allowed. Downloading code or recieving outside coding help is not allowed. Students are not allowed to copy writeups from other students or have help in writeups from web resources or outside parties. Anyone who gives code or writeups, or recievel them, is in violation of the integrity policy. Students who violate the policy may recieve punishments such as grade reduction or a note in the academic transcript.
- I urge students to report violations they suspect or become aware of.
- If the workload is so heavy that it is imnpossible to do in a reasonable amount of time, please report that to me as soon as possible.