Essential Information

As we all know, lots of information can be found on the web. Go to your favorite search engine (like the Yahoo site listed on my home page) and try searching on "financial mathematics" or "calculus refresher." See how many web pages you hit and visit a few interesting looking sites. As we cover specialized topics, try searching on them with keywords such as "option pricing".

Notes and FAQ

1/9/06: (Just to get the FAQ started) About significant digits...
I've been asked to explain what significant digits of an approximation to a number mean. Here goes: to get the number of significant digits, first *subtract* (rather than just looking at the numbers) the two (may as well be larger - smaller,) then find the position of the leading digit of the error relative to the position of leading digit of the exact answer. (We're thinking in fixed point representation in this discussion.) If the difference in that position is at most 5, then number of significant digits is one less than that position, else two less.

For example if 1.006 and .995 are used to approximate 1, calculate 1.006 - 1 = 0.006. Notice I put the zero in front of the decimal to start counting from the right position. There is disagreement at the 4th position, counting from the (base 10) position of the leading digit of 1, and the size of this disagreement is greater than 5, so this approximation has 2 significant digits. On the other hand, 1 - .995 = 0.004, which again first disagrees in the 4th position, and the size of the disagreement is at most 5, so .995 has 3 significant digits as an approximation to 1. BTW, it's also perfectly correct to say that each answerhas one significant digit, though this doesn't give all the available information. Hope this helps.

Class Policy Statement

Course: JDEP 384H, Numerical Methods in Business

Place/Time: 110 Kauffman, 9:30-10:45 TR, Spring 2007

Preq: Permission.

Objectives: To help students achieve competence in the following areas:

• Understanding of mathematical formulations of financial and business models that are amenable to numerical techniques.
• Knowledge of a cross-section of numerical techniques available for solving these financial and business models.
• Efficiency and reliability of algorithms.
• Implementation of algorithms via Matlab platform.
• Interpretation of computations (consistent with Hamming's dictum: The purpose of computing is insight, not numbers.)
Instructor: Dr. Thomas Shores

Telephone: Office 472-7233   Home 489-0560

Email: tshores1@math.unl.edu

Office Hours: Monday 2:00-3:30, Tuesday 11:00-12:30, Thursday 3:30-5:00, Friday 8:30-10:30, and by appointment. Office: 229 AvH

Class Attendance: Is required. If absent, it is incumbent upon the student to determine what has been missed as soon as possible. It is advisable to consult with the instructor.

Homework/Projects: Homework will be assigned in class and collected in accordance with the syllabus, and will be usually returned within one week. Although collaboration in solving most problems is encouraged, it is strictly forbidden to copy someone else's homework. It is expected that co-collaborators and other sources for the homework will be duly acknowledged. For some specified problems no collaboration will be allowed. The official programming language for this course is Matlab. Prior experience in Matlab is not required. Current information about the course will be available through Blackboard and the 384H homepage. Using the web is strongly recommended for keeping track of current activities in the course.

Reading Assignment: Read the sections of the texts as, or before, they are covered in class lectures. This is a standing assignment throughout the semester.

Grade: One midterm will be given and will account for 135 points. The final exam will count 140 points. Each exam may have a take home component. In-class exams are closed book with calculators. Homework will count 225 points. The final grade will be based on these 500 points.

Final Exam: Will be comprehensive. To be given on Tuesday, May 1, 10:00 - 12:00 am in 110 Kauffman.

Grades of "I", "W" or "P": These grades will be given in strict accordance with University policy. (See any Schedule of Classes for the relevant information and dates.)

Keep This Information!!!

Syllabus for JDEP 384H, Spring 2007

• TEXT:Introduction to Operations Research, Eighth Edition, Frederick Hillier and Gerald Lieberman, McGraw-Hill, New York, 2005.
ISBN: 0-07-252744-7

• The times listed below are approximate, and may be adjusted as the semester progresses. The two sources for material are the class textbook (BT) and my own prepared notes (NT). Assignments are due on Tuesday if they are listed first below, and Thursday otherwise. Unless otherwise stated, you should turn in hardcopy of your work. The specifics of each assignment will be given in class and posted on the web as the course progresses. Problems that are to be worked by individuals without collaboration will be marked ``(I)''. Each assignment will be worth 45 points. Each assignment includes all problems not yet collected and assigned one week or more before the due date.

 WEEK DATES SECTIONS TOPICS

 1 Jan 8-12 NT Introduction NT Matlab & Matrices NT Matlab & Calculus

 2 Jan 15 (no class) Martin Luther King Day Jan 16-19 NT Matlab & Calculus NT Matlab & Statistics

Friday, January 19, is the last day to withdraw from the course and not have it appear on your transcript.

 3 Jan 22-26 BT, Sec 2.1-2 Basic financial assets Asgn 1 due

 4 Jan 29-Feb 2 BT, Sec 2.3 Fixed income securities

 5 Feb 5-9 BT, Sec 2.3-4 Stock portfolio optimization

 6 Feb 12-16 BT, Sec 2.5-6 Asset and derivative pricing Asgn 2 due

 7 Feb 19-23 BT, 7.1-2 Option pricing by binomial lattices

 8 Feb 26-Mar 2 BT, 3.1-2 Numerical computation and linear systems

Friday, March 2, is the last day to change your grade option to or from ``Pass/No Pass''.

 9 March 5-9 Midterm BT, 3.3-4 Function approximation and system solving Asgn 3 due

 10 Mar 12-16 (no class) Spring Break

 11 Mar 19-23 BT, Sec 4.1-3 Monte Carlo methods and quadrature

 12 Mar 26-30 BT, Sec 4.4-6 Special techniques for MC simulation

 13 Apr 2-6 BT, Sec 8.1-3 Option pricing by MC methods Asgn 4 due

Friday, April 6, is the last day to withdraw from the course and receive a grade of W.

 14 Apr 9-13 NT Optimization in business

 15 Apr 16-20 NT Decision analysis
 16 Apr 23-27 NT Decision analysis Asgn 5 due Review

Final Exam: The final exam is a comprehensive exam to be given on Tuesday, May 1, 10:00 - 12:00 am in 110 Kauffman.

Department Grading Appeals Policy: The Department of Mathematics does not tolerate discrimination or harassment on the basis of race, gender, religion or sexual orientation. If you believe you have been subject to such discrimination or harassment please contact the department. If, for this or any other reason, you believe that your grade was assigned incorrectly or capriciously, appeals may be made to (in order) the instructor, the department chair, the departmental grading appeals committee, the college grading appeals committee and the university grading appeals committee.