Page 150 - buku panduan 20192020

Faculty of Science Handbook, Session 2019/2020

Premiums: expectation and variance of loss random SIQ3003 ACTUARIAL MATHEMATICS II
variable, fully continuous and discrete premiums,
semicontinuous premiums, m-thly premiums, gross Reserves: fully continuous and discrete reserves,
premiums, probabilities, percentiles. semicontinuous reserves, prospective and retrospective
reserves, expense reserves, variance of loss, special
Assessment: formulas, recursive formulas.
Continuous Assessment: 40%
Final Examination: 60% Markov Chains: discrete and continuous Markov chains,
Kolmogorov’s forward equations, premiums and reserves
Medium of Instruction: using Markov chains, multiple-state models.
English
Multiple Decrement Models: discrete and continuous
Soft Skills: decrement models, probability functions, fractional ages,
CS3, CTPS3 multiple and associated single decrement tables, uniform
assumption.
References:
1. Bowers, N., Gerber, H., Hickman, J., Jones, D., & Multiple Life Models: joint life, last survivor and contingent
Nesbitt, C. (1997). Actuarial mathematics (2 ed.). probabilities, moments and variance of multiple life models,
nd
Society of Actuaries. multiple life insurances and annuities.
2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
Actuarial mathematics for life contingent risks. Unit-linked contracts and profit tests: Emerging costs, profit
Cambridge University Press. testing for conventional and unit-linked contracts.
3. Cunningham, R. J. (2011). Models for quantifying risk.
Actex Publications. Assessment:
4. Promislow, S. D. (2011). Fundamentals of actuarial Continuous Assessment: 40%
mathematics. John Wiley & Sons. Final Examination: 60%

Medium of Instruction:
SIQ3002 PORTFOLIO THEORY AND ASSET MODELS English

Utility theory: Features of utility functions, expected utility Soft Skills:
theorem, risk aversion. CS3, CTPS3

Stochastic dominance: Absolute, first and second order References:
stochastic dominance. 1. Bowers, N., Gerber, H., Hickman, J., Jones, D., &
nd
Nesbitt, C. (1997). Actuarial mathematics (2 ed.).
Measures of investment risk: Variance, semi-variance, Society of Actuaries.
probability of shortfall, value-at-risk, expected shortfall. 2. Dickson, D. C., Hardy, M. R., & Waters, H. R. (2013).
Actuarial mathematics for life contingent risks.
Portfolio theory: Mean-variance portfolio, diversification, Cambridge University Press.
efficient frontier, optimal portfolio selection, efficient 3. Cunningham, R. J. (2011). Models for quantifying risk.
portfolio identification. Actex Publications.
4. Promislow, S. D. (2011). Fundamentals of actuarial
Models of asset returns: Single-index models, fitting a mathematics. John Wiley & Sons.
single index model, multi-index models.

Asset Pricing Model: Capital Asset Pricing Model, Arbitrage SIQ3004 MATHEMATICS OF FINANCIAL
Pricing Theory. DERIVATIVES

Efficient market hypothesis Introduction to derivatives: Call and put options, forwards,
futures, put-call parity.
Assessment:
Continuous Assessment: 40% Binomial models: one-step model, arbitrage, upper and
Final Examination: 60% lower bounds of options prices, construction of multi-step
binomial tree.
Medium of Instruction:
English The Black-Scholes model: Pricing formula, options Greeks,
trading strategies, volatility.
Soft Skills:
CS3, CTPS3 Hedging: Market making, delta hedging, Black-Scholes
partial differential equation, delta-gamma-theta
References: approximation
1. Elton, E. J., Gruber, M. J., Brown, S. J., & Goetzmann, Exotic options: Asian options, barrier options, compound
W. N. (2014). Modern portfolio theory and investment options, gap options, all-or-nothing options, exchange
th
analysis (9 ed.). John Wiley & Sons. options.
2. Bodie, Z., Kane, A., & Marcus, A. J. (2013).
th
Investment (10 ed.). McGraw-Hill/Irwin. Brownian motion and Itô’s lemma: Brownian motion, Itô’s
3. Francis, J.C., & Kim, D. (2013). Modern portfolio lemma, Sharpe ratio, martingale representation theorem
theory: Foundations, analysis, and new developments.
John Wiley & Sons. Term structure of interest rate: Vasicek model, Cox-
4. Joshi, M. S., & Paterson, J. M. (2013). Introduction to Ingersoll-Ross model, Black-Derman-Toy binomial tree
mathematical portfolio theory. Cambridge University
Press. Models for credit risk: Structural, reduced form and intensity
5. Bodie, Z., Merton, R.C., and Cleeton, D (2008). based models, Merton model, valuing credit risky bonds
Financial Economics, 2/E. Prentice Hall.

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