Math 4710/6710

MATHEMATICS of FINANCE

Math 4710/6710 is an introduction to the mathematics of interest and finance. We use the tools developed in calculus to study interest, finance, risk theory and other topics in business and finance. Some of the topics covered include: simple and compound interest, simple and compound discount, present and future value, force of interest, annuities, amortization schedules, insurance and risk theory, bonds and other securities and models of financial markets. A general introduction to actuarial science and financial analysis is given.

No prior knowledge of numerical methods and finite difference equations will be assumed, we will develop what is needed in the course. This course is applied mathematics (not a course in business or finance). The student will see the calculus and basic statistics applied to problems of interest They will learn the basics of the notation and mathematics used in finance and actuarial science.

Instructor: Dr. Calvin M. Burgoyne
642 Boyd Graduate Studies
542-5021 burgoyne@math.uga.edu
Text: The Theory of Interest 2nd Edition by Stephen G. Kellison Irwin Press 1991
References: Financial Economics H.H. Panjer Editor. The Actuarial Foundation

Course Outline:

1. The Measurement of Interest
Accumulation and Amount Functions
Effective rate, Simple and Compound Interest
Present and Future Value
Discount Rates
Force of Interest and Discount
Varying Interest

2. Solution of Problems of Interest
Numerical results
Time Periods
Equations of Value
Unknown Time and Unknown Rates of Interest
3. Annuities
Annuity-immediate, Annuity-due
Annuity Values
Perpetuities
Nonstandard terms
Unknown Time or Rate
Varying Interest
Annuities payable at different frequency than interest
Continuous Annuities
Varying Annuities
4. Yield Rates
Cash Flow Analysis
Borrowing and Lending Models
5. Amortization Schedules and Sinking Funds
Loan Balance
Amortization Schedules
6. Bonds and other Securities
Types of Securities
Price, Premium and Discount
Valuation
Practical Examples
7. Financial Analysis
Determination of Interest Rates
Inflation
Risk
Yield Curves
8. Insurance and Risk Models
Individual Risk Models
Survival Distributions and Life Tables
Life Insurance and Life Annuities
Risk Theory
9. Survey of Actuarial Exams
10. Pricing Models
Futures Contracts, Selling Short and Selling Long
Hedging and Hedge Funds
Currency Markets

Class: T/Th 2:00 - 3:15 322 Boyd

Office hours: M/W 2:30 - 3:30
T/Th 12:45 - 1:45

Midterm Exam # 1 Monday March 3

Midterm Exam # 2 Monday April 28

Final Exam Monday May 5 3:30 6:30

Grades:
Exam # 1 25%
Exam # 2 25%
Final 30%
Problems 20%