STAT1801 Probability and statistics: foundations of actuarial science
Textbooks
I. Miller & M. Miller: John E. Freund's Mathematical Statistics with applications (Pearson
Education International, 2004, 7th edition)
References
M. A. Bean: Probability: The Science of Uncertainty with Applications to Investments,
Insurance, and Engineering (Brooks/Cole, Thomas Learning)
S. Ghahramani: Fundamentals of Probability, with Stochastic Processes (2005, 3rd
edition)
S. M. Ross: A First Course in Probability (2005, 7th edition)
Course Contents
1. General Probability
- Basic elements of probability in set notation
- Mutually exclusive events
- Addition and multiplication rules
- Independence of events
- Combinatorial probability
- Conditional probability and expectations
- Bayes Theorem / Law of total probability
- Random variables
2. Univariate probability distributions (including binomial, negative binomial, geometric,
hypergeometric, Poisson, uniform, exponential, chi-square, beta, Pareto, lognormal,
gamma, Weibull and normal) and bivariate normal distribution
- Probability functions and probability density functions
- Cumulative distribution functions
- Mode, median, percentiles and moments
- Variance and measures of dispersion
- Central Limit Theorem
3. Sampling distributions and introduction of estimation
STAT1802
Financial mathematics
Textbooks
Broverman, S. A.:
Mathematics of Investment and Credit (ACTEX Publications - Mad River Books:
Connecticut, 2004, 3rd edition)
McDonald, R. L.: Derivatives Markets (Addison-Wesley: New York, 2005, 2nd edition)
References
Kellison, S. G.: The Theory of Interest (Irwin: Illinois, 1991, 2nd edition)
Key topics include:
1.
measurement of interest, annuities certain;
2.
discounted cash flow analysis;
3.
yield rates;
4.
amortization schedules and sinking funds;
5.
bonds and related securities;
6.
practical applications such as real estate mortgage, short sales and modern financial
instruments;
7.
stochastic approaches to interest;
8.
financial derivatives including forwards, futures, options and
swaps;
9.
insurance, collars and other strategies;
10. introduction to risk management.