1. Instructor:
Dr. Tao Pang Office: Harrelson Hall
226
Telephone: 513-2110
Email: tpang@ncsu.edu
Office hours: T, Th
2:00pm-2:55pm or by appointment.
2. Prerequisites: Knowledge of calculus and probability is assumed, although the student may take a probability class concurrently.
3. Textbooks:
- Actuarial Mathematics by Bowers, Gerber, Hickman, Jones and
Nesbitt, 2nd Ed. /1997.
- The Theory of Interest by Stephen Kellison, 3nd Ed./2008.
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.
5. Outline of Course:
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
6. Reading Schedule: The theory of interest and annuities can be found in the chapters of Kellison’s The Theory of Interest dealing with the measurement of interest and annuities. In particular, the students are encouraged to read the following parts: Chapters 1 (1.2-1.10), 2 (2.3-2.6), 3 (3.2-3.8). 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. We are going to cover the following chapters/sections in Actuarial Mathematics: Chapter 3, Sections 3.1-3.5; Chapter 4, Sections 4.1-4.4; Chapter 5, Sections 5.1, 5.3, 5.4; Chapter 6, Sections 6.1(excluding utility-theory approach), 6.3, 6.4; Chapter 7, Sections 7.1(excluding utility-theory approach), 7.4-7.6.
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 in one week or so as stated. Late homework should be avoided and they may only get partial credits. Some of the homework problems may involve Excel spread-sheets. Students are allowed to consult with other students or with the instructor on the homework.
The first in-class examination (September 30, Tuesday) covers compound interest and failure time distributions. The second in-class examination (November 6, Thursday) covers present value models and the results obtained from these models. The final examination (December 11, Thursday, 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:
8. Attendance Policy: The attendance policy is consistent with the Academic Regulations which can be found at http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.3.php
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/policies/student_services/student_discipline/POL11.35.1.php
10. Disability Services for Students: Students with a disability must contact the NCSU Disability Services. Additional information: http://www.ncsu.edu/equal_op/dss/