SECOND YEAR
Acad Unit: 4.0
Pre-requisite: Nil
The survival model and table. Select, ultimate and aggregate mortality tables. Annuities, assurance, premiums. Functions other than yearly. Policy values. Surrender and paid-up values, bonus and special policies. Stationary population. Stochastic approach to life insurance. Probability function of curtate future lifetime and probability density function of complete future lifetime. Expected cash flow under financial contracts involving death and survival. Use of cash flow model to determine product prices and reserves with sensitivity analysis. Run-off triangle and projecting the ultimate position in general insurance. No claim discount (NCD) system. Probability of claim.
Acad Unit: 4.0
Pre-requisite: Nil
Theory of interest rates: the rate of interest, force of interest, accumulated and present values. Basic compound interest functions: the equation of value and yields on a transaction, various types of annuities. Nominal rates of interest: interest and annuities payable p times per period. Discounted cash flow: net cash flows, net present values and yields. Capital redemption policies: calculation of premium, policy, surrender and paid-up values and policy alterations. The valuation of securities: fixed interest securities and ordinary shares, prices and yields, perpetuities, Makeham’s formula and optional redemption dates. Capital gains tax: valuation allowing for CGT. Cumulative sinking funds: relationship between successive capital repayments, the term of the loan. Yield curves: the discounted mean term, volatility, matching and immunisation. Consumer credit: flat rate of interest, early repayment terms, the rule of 78. Stochastic rate models: independent annual rates of return, simulation techniques, dependent rate of return.
Acad Unit: 4.0
Pre-requisite: AB103
Descriptive statistics. Random variables. Probability distributions. Expectations. Moment generating functions and cumulants. Independence and convolution. Functions of random variables. Conditional expectation and compound distribution. Central Limit Theorem. Random sampling and sampling distributions. Point and interval estimation. Testing of hypotheses; one and two sample problems; chi-square tests. Analysis of variance. Linear regression and correlation analysis
Acad Unit: 4.0
Pre-requisite: AB103
Life time random variable (distribution, density and survival function, hazard rate, life expectancy); estimation for censored lifetime data (Kaplan-Meier and Nelson-Aalon estimate, Cox model); multiple state models, estimators of transition intensities; Binomial model of mortality; test of consistency of estimates and graduation of rates; assurance and annuity contracts (moments of the present value of payments, commutation functions; random future loss and equivalence principle; net premium, reserve policy value.
Acad Unit: 4.0
Pre-requisite: AB103
Deterministic and stochastic models; sensitivity testing; stochastic process; Markov chain and process; Kolmogorov equations; Poisson process; sickness and marriage models; univariate time series models (ARIMA). Box-Jenkins procedure; transfer function and multivariate autoregressive models; Gauss-Wiener process; Monte Carlo simulation.
Acad Unit: 4.0
Pre-requisite: Nil
Contingent cash flow models. Compound interest, discounting and time value of money. Nominal and effective interest rates. Effects of inflation. Actuarial functions. Equation of value. General loan schedule. Discounted cash flow and investment project appraisal. Valuation of fixed interest securities and index-linked bonds. Effects of income and capital gains tax. Optional redemption dates. Pricing forward contracts. Term structure of interest rates. Duration, convexity and immunisation. Stochastic interest rate models.
Acad Unit: 4.0
Pre-requisite: Nil
Historical review of computers and their usage in Actuarial Science. Programming concepts; common programming languages in actuarial applications. Database concepts; spreadsheets; actuarial applications softwares.
FINAL YEAR
BA302 APPLIED ACTUARIAL STATISTICS
Acad Unit: 4.0
Pre-requisite: BA203
Loss distributions with and without reinsurance arrangements moments and moment generating functions (where defined) of the gamma, exponential, Pareto, generalised Pareto, normal, lognormal, Weibull and Burr distributions; fitting loss distributions; concepts of deductibles and retention limits; proportional and excess of loss reinsurance; claim amounts distributions of insurer and reinsurer under reinsurance. Risk models for short-term insurance contracts compound Poisson, compound binomial and compound negative binomial distributions; aggregate claims distributions. Ruin theory the adjustment co-efficient; Lundberg's inequality; effect on the probability of ruin of changing parameter values; effect of simple reinsurance arrangements. Credibility theory "American Credibility", Bayesian approach to credibility theory and empirical Bayes credibility theory; credibility premium formulae derived from the empirical Bayes credibility approach.
BA303 MORTALITY INVESTIGATIONS
Acad Unit: 4.0
Pre-requisite: Nil
Concepts of rates and other indices, statistical models for a single decrement, analysis of experience data, determination of the exposure to risk by the direct and the census methods, calculation of mortality and other decremental rates (including multiple decrement rates), selection. Graduation methods and their applications, tests of graduation, sources and collection of mortality and other actuarial data. Principal features of the UK general population mortality experience. Principal factors affecting variation of mortality. Standardised mortality ratios. Standard actuarial tables in common use.
Acad Unit: 4.0
Pre-requisite: BA205
Joint life and last survivor statuses. Contingent functions and reversionary annuities. Mulitple-decrement model. Pension fund benefits and contributions. Manchester Unity sickness functions. Pricing, costing options, reserving, surrender, alteration, paid-up and interchanging benefits of life, general and pensions business. Profit test and sensitivity analysis of life insurance and general insurance products.
BA333 SOCIAL SECURITY & PENSION FUNDS
Acad Unit: 4.0
Pre-requisite: BA205 & BA214
Social security in Singapore, the CPF and the various CPF social security schemes. Introduction to demography - population dynamics and population projections. General background to pension funds, methods of providing pensions, funded and unfunded schemes, state schemes, trust deed and rules, benefit structure and design, funding methods, valuation procedures, data bases for valuing assests and liabilities, interpretation of results, analysis of surplus, valuation report, asset/liability matching.
Acad Unit: 4.0
Pre-requisite: BA205
The insurance market. Administration of a life office. New business acquisition and policy servicing. Life insurance law. Financial background. Taxation and analysis of expenses. Mortality and morbidity. Reinsurance. Product pricing: conventional and unit-linked business. Actuarial investigations. Analysis and distribution of surplus. Role of the Appointed Actuary and professional code of conduct.
BA335 ACTUARIAL ASPECTS OF GENERAL INSURANCE
Acad Unit: 4.0
Pre-requisite: BA206
The nature of general insurance contacts. Legislation of general insurance companies in Singapore: investment and taxation principles. Documentation and data collection. Principles and techniques of rate making: rating structures, claims estimation models. Expense analysis. Valuation of assets and liabilities. Nature and purpose of reinsurance.