Page 131 - Handbook Bachelor Degree of Science Academic Session 20202021

Faculty of Science Handbook, Academic Session 2020/2021

Premiums: expectation and variance of loss random variable, 5. Bodie, Z., Merton, R.C., and Cleeton, D (2008).
fully continuous and discrete premiums, semicontinuous Financial Economics, 2/E. Prentice Hall.
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,
Soft Skills: Kolmogorov’s forward equations, premiums and reserves
CS3, CTPS3 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 (2 ed.). multiple and associated single decrement tables, uniform
nd
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:
SIQ3002 PORTFOLIO THEORY AND ASSET MODELS Continuous Assessment: 40%
Final Examination: 60%
Utility theory: Features of utility functions, expected utility
theorem, risk aversion. Medium of Instruction:
English
Stochastic dominance: Absolute, first and second order
stochastic dominance. Soft Skills:
CS3, CTPS3
Measures of investment risk: Variance, semi-variance,
probability of shortfall, value-at-risk, expected shortfall. References:
1. Bowers, N., Gerber, H., Hickman, J., Jones, D., &
nd
Portfolio theory: Mean-variance portfolio, diversification, Nesbitt, C. (1997). Actuarial mathematics (2 ed.).
efficient frontier, optimal portfolio selection, efficient portfolio Society of Actuaries.
identification. 2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
Actuarial mathematics for life contingent risks.
Models of asset returns: Single-index models, fitting a single Cambridge University Press.
index model, multi-index models. 3. Cunningham, R. J. (2011). Models for quantifying risk.
Actex Publications.
Asset Pricing Model: Capital Asset Pricing Model, Arbitrage 4. Promislow, S. D. (2011). Fundamentals of actuarial
Pricing Theory. mathematics. John Wiley & Sons.

Efficient market hypothesis.
SIQ3004 MATHEMATICS OF FINANCIAL
Assessment: DERIVATIVES
Continuous Assessment: 40%
Final Examination: 60% Introduction to derivatives: Call and put options, forwards,
futures, put-call parity.
Medium of Instruction:
English Binomial models: one-step model, arbitrage, upper and
lower bounds of options prices, construction of multi-step
binomial tree.
Soft Skills:
CS3, CTPS3 The Black-Scholes model: Pricing formula, options Greeks,
trading strategies, volatility.
References:
1. Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, Hedging: Market making, delta hedging, Black-Scholes
W. N. (2014). Modern portfolio theory and investment partial differential equation, delta-gamma-theta
th
analysis (9 ed.). John Wiley & Sons. approximation.
2. Bodie, Z., Kane, A., & Marcus, A. J. (2013). Investment
th
(10 ed.). McGraw-Hill/Irwin. Exotic options: Asian options, barrier options, compound
3. Francis, J.C., & Kim, D. (2013). Modern portfolio theory: options, gap options, all-or-nothing options, exchange
Foundations, analysis, and new developments. John options.
Wiley & Sons.
4. Joshi, M. S., & Paterson, J. M. (2013). Introduction to Brownian motion and Itô’s lemma: Brownian motion, Itô’s
mathematical portfolio theory. Cambridge University lemma, Sharpe ratio, martingale representation theorem.
Press.

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