MATH 605 Course Syllabus - fall 2012

NJIT Academic Integrity CODE:  All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly.  This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

 

Math 605:  Stochastic Calculus

 

Number of Credits:  3

 

Course Description:  This course provides an introduction to stochastic calculus. Topics include conditioning, Poisson processes, martingales, Brownian motion, Ito integrals, Ito's formula, stochastic differential equations, Feynman-Kac formula, Girsanov's theorem, and the martingale representation theorem. Financial applications include pricing, hedging, and interest rate models. Effective From: Fall 2010.

Prerequisites: Prior coursework in probability and differential equations as well as departmental approval.

Textbook: Stochastic Calculus for Finance II: Continuous Time Models by Steven Shreve.

References:

▪  C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, Springer, 2004.

▪  M. Grigoriu, Stochastic Calculus : Applications in Science and Engineering, Birkhauser, 2002.

▪  J. Steele, Stochastic Calculus and Financial Applications , Springer, 2001.

Instructor:   (for specific course-related information, follow the link below)

 

Math 605-101

Prof. Horntrop

 

Grading Policy:  The final grade in this course will be determined as follows: 

Homework, Quizzes & Projects:

35%

Midterm Exam:

30%

Final Exam:

35%


 

Drop Date: Please note that the University Drop Date November 6, 2012 deadline will be strictly enforced.

NJIT Honor Code Policy:  The NJIT Honor Code applies to all activities associated with the course, including but not limited to homework, quizzes, examinations, and projects. As an example, when you submit a homework assignment, you are certifying that your paper contains only your work and is not copied from other people or sources.

Examinations: There will be a midterm examination and a final examination. The midterm examination will occur before the "drop'' deadline. The final examination date, time, and location will be determined by the university.

Homework Policy:  Homework assignments/projects will be given frequently. Each assignment must be turned in at the beginning of class. Late assignments are NOT accepted. Early assignments are always welcomed and are appropriate for preplanned absences from class. As a standing assignment, you should read the relevant sections of the textbook prior to lecture.

Quiz Policy:  From time to time, quizzes may be given. Make up quizzes are NOT given.

Attendance Policy:  Attendance at and participation in all lectures is expected. If you know in advance that you will be absent from class for a legitimate reason, please tell me prior to your absence so that appropriate arrangements (if any) can be made. Tardiness to class is very disruptive of the classroom environment and should be avoided.

Makeup Exam Policy:  There will be No make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.

Further Assistance:  For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.

Cellular Phones:  All cellular phones and beepers must be switched off during all class times.


 

MATH DEPARTMENT CLASS POLICIES LINK 

All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.

September 3, 2012

M

Labor Day ~ No classes

November 6, 2012

T

Last Day to Withdraw from this course

November 20, 2012

T

Classes follow a Thursday Schedule

November 21, 2012

W

Classes follow a Friday Schedule

November 22-25, 2012

R-Su

Thanksgiving Recess

December 13, 2012

R

Reading Day

December  14-20, 2012

F- R

Final Exams

 

Course Topics:

 

Week

 

Course Topics

 

Week 1


 

 

     Review of Conditioning

 

 

     Martingales

     Brownian Motion

     Ito Integrals

     Ito's Formula

 

 

     Stochastic Differential Equations

 

 

     Girsanov's Theorem

     Martingale Representation Theorem

     Feynman-Kac Formula

 

 

     Applications to Pricing and Interest Rate Models

 

 

Week 2

 

Week 3

 

Week 4

 

Week 5

 

Week 6

Week 7

Week 8

 

Week 9

 

Week 10
 

Week 11

Week 12

Week 13

Week 14

 

Finals

 

Final EXAM WEEK:  December 14-20, 2012

 

Prepared By:  Prof. David Horntrop

Last revised:  June 1, 2012

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