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Faculty of Science Handbook, Session 2017/2018

Life Insurances: continuous type life insurances, discrete 2. Bodie, Z., Kane, A., and Marcus, A. J. (2013).
type life insurances, probabilities, percentiles, recursive Investment 10/E. McGraw-Hill/Irwin.
formula, m-thly payments, varying insurance. 3. Francis, J.C., and Kim, D. (2013). Modern Portfolio
Theory: foundations, analysis, and new developments.
Life Annuities: continuous type life annuities, discrete type John Wiley & Sons.
life annuities, expectation and variance, probabilities, 4. Joshi, M. S., and Paterson, J. M. (2013). Introduction
percentiles, recursive formulas, m-thly payments, varying to Mathematical Portfolio Theory. Cambridge
annuities. University Press.
5. Bodie, Z., Merton, R.C., and Cleeton, D (2008).
Premiums: expectation and variance of loss random Financial Economics, 2/E. Prentice Hall.
variable, fully continuous and discrete premiums, .
semicontinuous premiums, m-thly premiums, gross
premiums, probabilities, percentiles.
SIQ3003 ACTUARIAL MATHEMATICS II
Assessment:
Continuous Assessment: 40% Reserves: fully continuous and discrete reserves,
Final Examination: 60% semicontinuous reserves, prospective and retrospective
reserves, expense reserves, variance of loss, special
Medium of Instruction: formulas, recursive formulas.
English
Markov Chains: discrete and continuous Markov chains,
Humanity Skill: Kolmogorov’s forward equations, premiums and reserves
CS3, CT3 using Markov chains, multiple-state models.
References: Multiple Decrement Models: discrete and continuous
1. Bowers, N., Gerber, H., Hickman, J., Jones, D., decrement models, probability functions, fractional ages,
Nesbitt, C. (1997). Actuarial mathematics, 2nd ed., multiple and associated single decrement tables, uniform
Society of Actuaries. assumption.
2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
Actuarial mathematics for life contingent risks. Multiple Life Models: joint life, last survivor and contingent
Cambridge University Press. probabilities, moments and variance of multiple life models,
3. Cunningham, R. J. (2011). Models for quantifying risk. multiple life insurances and annuities.
Actex Publications.
4. Promislow, S. D. (2011). Fundamentals of actuarial Unit-linked contracts and profit tests: Emerging costs, profit
mathematics. John Wiley & Sons. testing for conventional and unit-linked contracts.
Assessment:
Continuous Assessment: 40%
SIQ3002 PORTFOLIO THEORY AND ASSET MODELS Final Examination: 60%
Utility theory: Features of utility functions, expected utility Medium of Instruction:
theorem, risk aversion. English
Stochastic dominance: Absolute, first and second order Humanity Skill:
stochastic dominance. CS3, CT3
Measures of investment risk: Variance, semi-variance, References:
probability of shortfall, value-at-risk, expected shortfall. 1. Bowers, N., Gerber, H., Hickman, J., Jones, D.,
Nesbitt, C. (1997). Actuarial mathematics, 2 nd ed.,
Portfolio theory: Mean-variance portfolio, diversification, Society of Actuaries.
efficient frontier, optimal portfolio selection, efficient 2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
portfolio identification. Actuarial mathematics for life contingent risks.
Cambridge University Press.
Models of asset returns: Single-index models, fitting a 3. Cunningham, R. J. (2011). Models for quantifying risk.
single index model, multi-index models. Actex Publications.
4. Promislow, S. D. (2011). Fundamentals of actuarial
Asset Pricing Model: Capital Asset Pricing Model, Arbitrage mathematics. John Wiley & Sons.
Pricing Theory.

Efficient market hypothesis SIQ3004 MATHEMATICS OF FINANCIAL
DERIVATIVES
Assessment:
Continuous Assessment: 40% Introduction to derivatives: Call and put options, forwards,
Final Examination: 60% futures, put-call parity.

Medium of Instruction: Binomial models: one-step model, arbitrage, upper and
English lower bounds of options prices, construction of multi-step
binomial tree.
Humanity Skill:
CS3, CT3 The Black-Scholes model: Pricing formula, options Greeks,
trading strategies, volatility.
References:
1. Elton, E. J., Gruber, M. J., Brown, S. J., and Hedging: Market making, delta hedging, Black-Scholes
Goetzmann, W. N. (2014). Modern Portfolio Theory partial differential equation, delta-gamma-theta
and Investment Analysis. 9/E. John Wiley & Sons. approximation

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