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Math 605: Stochastic Calculus
Fall 2018 Graduate Course Syllabus

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.

Course Information

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.

Number of Credits: 3

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

Course-Section and Instructors

Course-Section Instructor
Math 605-101 Professor D. Horntrop

Office Hours for All Math Instructors: Fall 2018 Office Hours and Emails

Required Textbooks:

Title Stochastic Calculus for Finance II: Continuous Time Models
Author Shreve
Edition 1st
Publisher Springer
ISBN # 0387401010
  • 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.
  • ExtraInfo

    University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 12, 2018. It will be strictly enforced.


    DMS Course Policies: 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.

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

    Homework, Quizzes, and Projects 30%
    Midterm Exam 35%
    Final Exam 35%

    Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced. 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.

    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.

    Exams: 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.

    Midterm Exam TBA
    Final Exam Period December 15 - 21, 2018

    The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

    Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

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

    Additional Resources

    Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

    If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at The office is located in Fenster Hall, Room 260.  A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

    For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

    Important Dates (See: Fall 2018 Academic Calendar, Registrar)

    Date Day Event
    September 4, 2018 T First Day of Classes
    September 10, 2018 M Last Day to Add/Drop Classes
    November 12, 2018 M Last Day to Withdraw
    November 20, 2018 T Thursday Classes Meet
    November 21, 2018 W Friday Classes Meet
    November 22 - 25, 2018 R - Su Thanksgiving Recess
    December 12, 2018 W Last Day of Classes
    December 13 & 14, 2018 R & F Reading Days
    December 15 - 21, 2018 Sa - F Final Exam Period

    Course Outline

    Week 17Course Topics
    • 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
    FINAL EXAM WEEK: DECEMBER 15 - 21, 2018

    Updated by Professor D. Horntrop - 8/31/2018
    Department of Mathematical Sciences Course Syllabus, Fall 2018