2. Prerequisites: Knowledge of calculus and probability is assumed, although the student may take a probability class concurrently.
3. Textbook:
- Actuarial Mathematics by
Bowers,
Gerber, Hickman, Jones and Nesbitt,
2nd Ed. /1997.
- The Theory of Interest by
Stephen Kellison, 2nd Ed./1991.
4. Course Objectives:
In this course students learn how to formulate and apply present value
models incorporating future contingent payments and failure time random
variables. Since economic considerations, such as interest rates,
often play a dominant role in long-term modeling, the course also
introduces
the student to the various quantitative measures of compound interest
and
annuities. Students will learn how to calculate a variety of
compound
interest and actuarial functions using current software
5. Outline of Course:
Calculus-Based Compound Interest: (6 classes) Theory of
compound interest in both finite 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
Failure Time Distributions: (4 classes) 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: (10 classes) 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: (7 classes) 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
6. Reading Schedule
There are no reading assignments during the study of the theory of
interest. The basis of this material can be found in the chapters of
Kellison’s
The
Theory of Interest dealing with the measurement of interest and
annuities. Students are referred to this textbook for additional
insights and exercises.
The development of long-term models for risk management systems follows the approach taken in the Actuarial Mathematics textbook. The topics that we cover correlate to the chapters in Actuarial Mathematics as follows:
Failure Time
Distributions:
Chapter 3
Formulating Present
Value Models:
Chapters 4 and 5
Obtaining Results
from Present Value Models:
Chapters 6 and 7
Students use the textbook for solving homework problems and developing a deeper understanding of the material presented in class, but there is no formal reading schedule.
7. Homework/Exam Schedule and Grade Policy
Homework sets will be assigned weekly, and the solutions are due next
TUESDAY
class meeting. Late homework should be avoided and they only get
partial
credits. Some of the homework problems may involve Excel
spreadsheets.
Students are allowed to consult with other students or with the
instructor
on the homework. Assignments are graded by the instructor and
returned
promptly.
The first in-class examination (September 23, Thursday) covers compound interest and failure time distributions. The second in-class examination (November 4, Thursday) covers present value models and the results obtained from these models. The final examination (December 7, Tuesday, 1:00pm-4:00pm) covers the work of the entire semester. All the in-class and final exams are close-book.
No Make-Up Test will be given. In very special cases, a make-up test might be given during the final exam period.
The final grade is determined as the follows:
9. Academic Integrity
Plagiarism and cheating are attacks on the very foundation of academic
life, and cannot be tolerated within universities. Section eight (8) of
the Code defines academic dishonesty and provides information on
potential
sanctions for violators of academic integrity. The NCSU Academic
Integrity
statement can be found at
http://www.ncsu.edu/provost/academic_policies/integrity/reg.htm
10. Disability Services for Students
Students with a disability must contact the NCSU Disability Services.
Additional information: http://www.ncsu.edu/equal_op/dss/.