UNIVERSITY OF THE WITWATERSRAND, JOHANNESBURG

Third Year Courses

STAT3017 MATHEMATICAL STATISTICS III (72 POINTS)
Third qualifying course
Mathematical Statistics III consists of the courses: - Inference; Applied Statistics; Stochastic Processes; Regression and Time Series; Risk Theory IIIA and IIIB.
Detailed syllabuses of the above courses are given below.
Subject to the approval of the Head of the School, another course within the Mathematical Sciences may replace one of the courses.

STAT3003 REGRESSION AND TIME SERIES III (12 POINTS)
Qualifying course
Multiple regression includes theory, as well as aspects for assessing model fit, such as residual analysis, outlier diagnostics and problems of model interpretation due to multicollinearity. The time series section covers the theory and application of Box Jenkins times series methods, including model building and model checks.

STAT3004 STOCHASTIC PROCESSES III (12 POINTS)
Qualifying course
The course consists of an Introduction to Markov chains: equivalence classes of states, exact and limiting distributions, mean and variance of sojourn times, and applications. Continuous time: includes birth and death processes, extinction probabilities, queueing theory, and renewal.

STAT3005 APPLIED STATISTICS III (12 POINTS)
Qualifying course
Applied Likelihood Methods; Generalised Linear Models; Resampling Models;
Categorical Data Analysis.

STAT3007 INFERENCE III (12 POINTS)
Qualifying course
a) Quality improvement and control: Shewart Control Chart; General Factorial and 2k Designs etc.; Sequential Analysis.
b) Nonparametric Methods: C.I.?s for percentiles; various tests.
c) Likelihood Theory: sufficiency; asymptotic normality; information matrix.

STAT3008 ACTUARIAL SCIENCE III (72 POINTS)
Third qualifying course
The course comprises a selection of courses totaling 72 points. The choice of courses is subject to the approval of the Head of School and may vary from year to year.
A student must successfully complete Computer Studies for Actuaries III and at least 48 points from the following courses: Life contingencies III; Actuarial Economics; Survival Models; Risk Theory IIIA; Risk Theory IIIB.
No more that 12 points from an appropriate mathematical or financial third year level course may be taken.

STAT3009 COMPUTER STUDIES FOR ACTUARIES III (12 POINTS)
Qualifying course
Use of computers in actuarial work, both scientific and commercial.

STAT3010 LIFE CONTINGENCIES III (24 POINTS)
Qualifying course
The mathematics of life assurance and pension schemes.

STAT3013 RISK THEORY IIIA (12 POINTS)
Third qualifying course
The application of statistical models to insurance risks.

Course outline

1. Loss distributions (Lognormal, Weibul, Gamma, Pareto, Negative Exponential and the like) and MLE?s (Maximum Likehood estimates ? both one or two parameters)

2. Risk Models: A random sum of a random variable. Theory is presented (includes recursive formula and the translated Gamma Distribution). Also look at the case of having a Re insurer.

3. Experience rating: NCD?s (No Claim Discount Systems)

4. Claims Reserving: Chain Ladder Method, Average Cost per Claim Method and BF (Bornhuetter Ferguson) Method ? with and without claims inflation

5. Bayesian Statistics: Bayes theorem, Loss estimators (quadratic, absolute error, all-or-nothing), and prior, likehood and posterior distribution

6. Ruin Theory: Poisson process, Lundberg inequality, adjustment coefficient, Reinsurance (Proportional and non-proportional)

7. Credibility Theory: Basic concept and models (Gamma/Poisson, Normal-Normal), Two Empirical Models (both theory and numerical)

8. Decision Theory: Very basic introduction. Introduction to Statistical games, a decision function, a loss function and decision criteria (Minimax, Bayes criteria)

9. Generalised Linear Models: A basic knowledge is required in Risk Theory.

10. Comprehensive tutorial pack: Covers Institute/Faculty of Actuaries exams over the last 3 ? 4 years as well as Wits exams over the same period

11. A risk rating exercise is also given, where students can use Excel or Access to determine what the premium rates will be for a block of motor-vehicle claims, given a policy record dataset as well as a claims data set. Different risk factors are given, like age, gender, yes/no to having an immobiliser, etc.

STAT3014 RISK THEORY IIIB (12 POINTS)
Third qualifying course
The application of statistical models to insurance risks.