Syllabus for MA 412, Fall 2009

1. Instructor: Jeffrey S. Scroggs

Office Hours: Posted at http://www4.ncsu.edu/~scroggs/mywebsite/OfficeVisits.html.
E-mail address: scroggs@ncsu.edu
Office: SAS 2108 B
Phone Number: 919.515.7817
Home page: http://www4.ncsu.edu/~scroggs/mywebsite
Class meeting times: TuTh, 3:00-4:15, 2225 SAS Hall

Communication: Students will be notified via email of announcements associated with this course.  The email address registered with the NCSU online directory will be used for this purpose.  It is the student's responsibility to maintain a valid email address and check the email sent to it.

2. Requisites

Prerequisite: MA 241 or MA 231, Corequisite: MA 421, BUS(ST) 350, ST 301, ST 311, ST 361, ST 370, ST 371, ST 380 or equivalent

3. GER Statement

This class does not satisfy a General Education Requirement

4. Student learning outcomes for the course.

1. Students will acquire a practical knowledge of the theory of interest in both finite and continuous time, and will be able to apply the concept of present value to the building of actuarial models on future contingent cash flows and failure time random variables.
2. Students will be able to
1. Explain the difference between a stochastic and a deterministic model and identify the advantages/disadvantages of each.
2. Determine the characteristics of the components and the effects of changes to the components of actuarial models. Components include a deterministic interest rate structure, a scheme for the amounts of the cash flows, a probability distribution of the times of the cash flows, and the probability distribution of the present value of the set of cash flows
3. Apply the equivalence principle to a model to associate a pattern of costs with a set of future contingent cash flows.
4. Characterize discrete and continuous univariate probability distributions for failure time rand variables in terms of the life table functions, the cumulative distribution function, the survival function, the probability density function, and the hazard function (force of mortality), as appropriate, and establish relations between the different functions.
3. Students will be able to determine an appropriate model for a given business problem. Business applications include premium rates for life insurance and annuity contracts, benefit reserves for insurance contracts, cost of a warranty for manufactured goods, and value of a financial instrument such as a loan or stock.

5. Textbooks (including links to sample answers, etc.)

(Official NCSU Textbook link)

6. Course organization and scope and projected schedule of reading assignments.

Compound Interest and Basic Annuities: Theory of compound interest in both discrete and continuous time; application of concepts of present value and accumulated value to various streams of cash flow; nominal and effective interest and discount rates, and the force of interest; annuity-immediate and annuity-due

Failure Time Distributions: Discrete and continuous univariate probability distributions for failure time random variables, and their relation to life table functions, survival functions, and the force of mortality

Formulating Present Value Models (Life Insurance and Life Annuities): Formulating models (stochastic and deterministic) for the present value, with respect to an assumed deterministic interest rate structure, of a set of future contingent cash flows; characteristics of the probability distributions of the times of the cash flows and the present value of the set of cash flows

Obtaining Results from Present Value Models (Benefit Premiums and Benefit Reserves): Associating a pattern of costs with a set of future contingent cash flows; the evolution of liabilities under the cost pattern adopted; applications to insurance, health care, credit risk, environmental risk, consumer behavior, and warranties

8. Projected schedule of reading, homework due dates, quizzes and tests (link to HW problems).

(Extra) HW problems are assigned for some sections (follow this link). The link is also in the spreadsheet linked above.

Sample solutions to the extra HW problems have been linked to the webpage where they are posted.

Note: the 'projected' becomes the 'actual' as the semester progresses.

9. Grades

Scores and grades will be posted at Vista (follow this link).

Percent Range	Grade
97.6 <= X <= 100	A+
92.3 <= X < 97.6	A
90.0  <= X < 92.3	A-
87.6 <= X < 90.0	B+
82.3 <= X < 87.6	B
80.0 <= X < 82.3	B-
77.6 <= X < 80.0	C+
72.3 <= X < 77.6	C
70.0 <= X < 72.3	C-
67.6 <= X < 70.0	D+
62.3 <= X < 67.6	D
60.0 <= X < 62.3	D-
X < 60	F

Quizes

New as of 27 August 2009: Homework will NOT be collected. Your homework grade has been replaced by a quiz grade. You can use your exam cheet sheet and/or calculator, but no other materials. The quiz will cover all the homework through the previous lecture. That means a quiz given on a Thursday will cover homework assigned the Tuesday, two days before, as listed in the assignments in the spreadsheet posted under item 8.

There will be 10 quizes. Quiz dates are posted under item 8.

The total you can earn on the 10 quizes is 30 points; however 20 points will be treated as 'perfect'.

Quiz grade = min((sum of quiz scores)/20, 10%)

Scoring Rubric (each quiz is graded out of 3 points)

3 points: conceptual understanding apparent; consistent notation, with only an occasional error; logical formulation; complete or near-complete solution/response
2 points: conceptual understanding only adequate; careless mathematical errors present (algebra, arithmetic, for example); some logical steps lacking; incomplete solution/response.
1 points: conceptual understanding not adequate; procedural errors; logical or relational steps missing; poor response or no response to the question posed.
0 points: does not attempt problem or conceptual understanding totally lacking.

Exams and Final Exam

Students that can work only the assigned problems on an exam should expect a C in the course; whereas, students that can work most (or all) the problems (and study the material) should expect an A or B. Some questions may come from examples in the book and some questions may come from the derivations.

The best way to earn a top grade is to (1) read the material before it is presented in class, (2) attend class and ask questions, (3) work homework after every class, and (4) form a study group to assist learning and homework completion.

Final Exam (new as of 23 November 2009)

Final exam will have 14 questions.

• 4 questions strongly based on questions from Exam 1
• 4 questions strongly based on questions from Exam 2
• 2 questions based on homework from Exams 1 & 2
• 4 questions from material covered after Exam 2
• Each question is worth 18 points. Even though your score may be above 200 points, the maximum score will be 200 points.

Replacing an exam score. If your final exam score divided by 2 is more than either exam, your exam score will be replaced by the final exam score (divided by 2).

• Example: (current Exam 1 score) = 96, (current Exam 2 score) = 95, (final Exam score) = 180, then
  • (new Exam 1 score) = 96, (new Exam 2 score) = 95, (final Exam score) = 180 (no change)
• Example: (current Exam 1 score) = 96, (current Exam 2 score) = 75, (final Exam score) = 180, then
  • (new Exam 1 score) = 96, (new Exam 2 score) = 90, (final Exam score) = 180 (Exam 2 score replaced)
• Example: (current Exam 1 score) = 76, (current Exam 2 score) = 75, (final Exam score) = 180, then
  • (new Exam 1 score) = 76, (new Exam 2 score) = 90, (final Exam score) = 180 (Exam 2 score replaced)

10. Incomplete grades, late assignments, and missed exams.

Late homework is accepted only if there is an excused absence.

Hourly Exams missed due to a excused absence will not be made up. Instead, the grade from the other exam will be used for the missing grade. If both exams are missed due to excused absences, then the final exam grade will be used for the missing grades.

11. Attendance, etc.

Excused Absence: NCSU policy, including what constitutes an 'Excused Absence,' is covered in REG 02.20.3. An absence will be 'excused' only after documentation of the situation is provided to the instructor.

H1N1, Fall 2009.

If you are ill with symptoms of influenza (i.e. fever over 100, sore throat, cough, stuffy or runny nose, fatigue, headache, body aches, vomiting and diarrhea) please do not come to class. Instead, immediately contact your medical provider or Student Health Services (515-7107) for advice or to arrange an appointment.

If you are diagnosed with H1N1, please inform Dr. Scroggs immediately (scroggs@ncsu.edu or 515-7817). You will be required be isolate away from class for up to 7 days or 24 hours after symptoms subside, whichever is longest.

If Student Health Services is unable to treat you, contact Dr. Scroggs via email for an alternative to Health Services documentation.

12. Academic Integrity.

Homework: Students are strongly encouraged to form study groups and turn in group homeworks (one paper for each group). Groups should be of size 2 to 3. Larger groups require prior approval from the instructor.

Exams: Students will neither give nor receive any assistance on any hourly or final exam. This means there is no use of electronic communication devices during exams, no student-to-student interactions, no wondering eyes, etc. Some students may be assigned seats for exams.

Exam cheet sheet: Each student can bring a single page of formulas to Hour Exams. The page cannot have worked problems, only formulas and the name of particular symbols (e.g. 'annuity-due') . The page can be no larger than 8 1/2 x 11 inches, and can have information on only one side. The page will be turned in with exam (and returned with the graded exam).

Any violation of this policy will be reported to the Office of Student Conduct, and will result in an F for this course.

13. Students with disabilities:

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG 02.20.1).

14. Laboratory safety/risk assumption:

There is no physical activity and no field trips associated with this course.

15. Statement on extra expenses:

There are no extra expenses related to this course.

16. Statement on transportation:

There are no field trips for this course.

17. Additional Links & Information

Life Tables from Social Security (link). I used data from Table 6 with birth year 1960. First, I saved the web page to my desktop, then I opened the saved page with MS Excel. Table used in class (link).

Matlab demo of Example 4.3.1

• ch4.m
• ex4p3p1.m (this is the file you run)
• iltable.m

Last revised 23-nov-09