Page 55 - handbook 20162017

Faculty of Science Handbook, Session 2016/2017

Markov models: Multi-state Markov models, Kolmogorov 2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
forward equations, estimation of the force of mortality, Actuarial mathematics for life contingent risks.
estimation of multi-state model transition intensities. Cambridge University Press.
3. Cunningham, R. J. (2011). Models for quantifying risk.
Binomial and Poisson models of mortality: Binomial model Actex Publications.
of mortality, uniform and constant force of mortality 4. Promislow, S. D. (2011). Fundamentals of actuarial
assumptions, maximum likelihood estimator for the rate of mathematics. John Wiley & Sons.
mortality, Poisson models.
Graduation and statistical tests: methods of graduating
crude estimates, Chi-square test, standardised deviation SIQ3002 PORTFOLIO THEORY AND ASSET MODELS
test, sign test, grouping of sign test, serial correlations test.
Utility theory: Features of utility functions, expected utility
Exposed to risk: Exact exposed to risk, approximate theorem, risk aversion.
exposed to risk using census data.
Stochastic dominance: Absolute, first and second order
Assessment: stochastic dominance.
Continuous Assessment: 40%
Final Examination: 60% Measures of investment risk: Variance, semi-variance,
probability of shortfall, value-at-risk, expected shortfall.
Medium of Instruction:
English Portfolio theory: Mean-variance portfolio, diversification,
efficient frontier, optimal portfolio selection, efficient
Humanity Skill: portfolio identification.
CS3, CT3
Models of asset returns: Single-index models, fitting a
References: single index model, multi-index models.
1. Elandt-Johnson, R. C., & Johnson, N. L. (1999).
Survival models and data analysis. John Wiley. Asset Pricing Model: Capital Asset Pricing Model, Arbitrage
2. Benjamin, B., & Pollard, J. H. (1993). The analysis of Pricing Theory.
mortality and other actuarial statistics. Institute and
Faculty of Actuaries. Efficient market hypothesis
3. London, Dick (1998). Survival Models and their
Estimation. ACTEX Publications. Assessment:
4. Peter J. Smith (2002). Analysis of Failure and Survival Continuous Assessment: 40%
Data. Chapman & Hall. Final Examination: 60%

Medium of Instruction:
SIQ3001 ACTUARIAL MATHEMATICS I English
Survival distributions: lifetime probability functions, force of Humanity Skill:
mortality, moments and variance, parametric survival CS3, CT3
models, percentiles, recursions, fractional ages, select and
ultimate life tables. References:
1. Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann,
Life Insurances: continuous type life insurances, discrete W. N. (2009). Modern portfolio theory and investment
type life insurances, probabilities, percentiles, recursive analysis. John Wiley & Sons.
formula, m-thly payments, varying insurance. 2. Dobbins, R., Witt, S. F., & Fielding, J. (1994). Portfolio
theory and investment management. 2nd Ed., Wiley-
Life Annuities: continuous type life annuities, discrete type Blackwell.
life annuities, expectation and variance, probabilities, 3. Joshi, M. S., & Paterson, J. M. (2013). Introduction to
percentiles, recursive formulas, m-thly payments, varying Mathematical Portfolio Theory. Cambridge University
annuities. Press.
4. Panjer, H. H. (1997). Financial Economics. Society of
Premiums: expectation and variance of loss random Actuaries Foundation.
variable, fully continuous and discrete premiums,
semicontinuous premiums, m-thly premiums, gross
premiums, probabilities, percentiles. SIQ3003 ACTUARIAL MATHEMATICS II

Assessment: Reserves: fully continuous and discrete reserves,
Continuous Assessment: 40% semicontinuous reserves, prospective and retrospective
Final Examination: 60% reserves, expense reserves, variance of loss, special
formulas, recursive formulas.
Medium of Instruction:
English Markov Chains: discrete and continuous Markov chains,
Kolmogorov’s forward equations, premiums and reserves
Humanity Skill: using Markov chains, multiple-state models.
CS3, CT3
Multiple Decrement Models: discrete and continuous
References: decrement models, probability functions, fractional ages,
1. Bowers, N., Gerber, H., Hickman, J., Jones, D., multiple and associated single decrement tables, uniform
Nesbitt, C. (1997). Actuarial mathematics, 2nd ed., assumption.
Society of Actuaries.

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