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CREDIBILITY THEORY AND LOSS DISTRIBUTIONS

Distributions useful for modeling insurance loss random variables. Approximations for and estimations of these loss distributions. Point and interval estimation, and test of statistical hypotheses.

Introduction to credibility theory, experience rating and claim reserving. Bayesian inferential techniques. Stochastic simulation and computational techniques.

 

Course Code: 
ACT 402
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 402 & ACT 302
Select Programme(s): 
Actuarial Science

SURVIVAL MODELS

Tabular Survival Models – Estimates from complete data samples, Estimates from incomplete data samples (sample design, moments procedures, maximum likelihood procedures).  Parametric Survival Models.
 

Course Code: 
ACT 401
No. of Credits: 
3
Level: 
Level 400
Course Semester: 
First Semester
Pre-requisite: 
STA 301 & ACT 301
Select Programme(s): 
Actuarial Science

LIFE CONTINGENCIES II

Net Premiums – Whole Life and Term Insurance, Endowments, Deferred Life Annuities, Premiums Paid m Times a Year, Policies with Premium Refund.

Net Premium Reserves – The Survival Risk, Net Reserve Premium for Whole Life, Net Premiums Reserve at Fractional Duration, Allocation of the Overall Loss to Policy Years,

Technical Gain, Procedure for Endowment and The Continuous Model. Multiple Decrements – An Introduction. Multiple Life Insurance.

 

Course Code: 
ACT 304
No. of Credits: 
3
Level: 
Level 300
Course Semester: 
Second Semester
Pre-requisite: 
ACT 301
Select Programme(s): 
Actuarial Science

LIFE CONTINGENCIES I

Basic Mathematics of Life Contingencies, Effective and Nominal interest rates. The Future Lifetime of a Life Aged x  (T) – Model, Force of Mortality, Analytic Distribution of T,

Curtate Future Lifetime of x, Life Tables, Probabilities of Death for Fractions of a Year.

Life Insurance – Whole Life and Term Insurances, Endowment, Insurance Payable at the Moment of Death, General Type of Life Insurance and Variable Life Insurance.

Life Annuities – Elementary, Payment made more Frequently than Once a Year, Variable Life Annuities, Standard Type of Life Annuities, Payment Starting at Non-integral Ages

 

Course Code: 
ACT 301
No. of Credits: 
3
Level: 
Level 300
Course Semester: 
First Semester
Pre-requisite: 
MAT 202 & MAT 203
Select Programme(s): 
Actuarial Science

FINANCIAL ANALYSIS & ECONOMICS

Yield curves, spot rates, forward rates, duration, convexity, and immunization. Derivatives, forwards, futures, short and long positions, cal and put options, spread, collars, hedging, arbitrage, and swaps.

 

Course Code: 
ACT 214
No. of Credits: 
3
Level: 
Level 200
Course Semester: 
Second Semester
Pre-requisite: 
MAT 102
Select Programme(s): 
Actuarial Science

MATHEMATICS OF INVESTMENT & CREDIT

Inflation; rates of interest [simple, compound (interest and discount), real, nominal, effective, dollar-weighted, time-weighted, spot, forward], term structure of interest rates; force of interest (constant and varying); equivalent measures of interest; yield rate; principal; equation of value; present value; future value; current value; net present value; accumulation function; discount function; annuity certain (immediate and due); perpetuity (immediate and due); stocks ( common and preferred); bonds (including zero-coupon bonds); other financial instruments such as mutual funds, and guaranteed investment contracts. Determining equivalent measures of interest; discounting; accumulating; determining yield rates; estimation the rate of return on a fund; and amortization.

 

Course Code: 
ACT 212
No. of Credits: 
3
Level: 
Level 200
Course Semester: 
First Semester
Pre-requisite: 
MAT 102
Select Programme(s): 
Actuarial Science

SURVIVAL DATA ANALYSIS

Survival function, hazard functions, cumulative hazard function, censoring. Kaplan-Meier survival curve, parametric models. Comparison of two groups – log-ranked test.

Inclusion of covariates – Cox P.H. model, application of model checking. Competing risks – extensions of Cox’s model.

 

Course Code: 
STA 810
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
Second Semester
Pre-requisite: 
STA 303
Select Programme(s): 
Statistics

CLINICAL TRIALS

Organisation and Planning: Protocol, patient selection, response Justification of  method for randomisation: Uncontrolled trials, blind trials, Placebo’s, ethical issues. The size of a clinical trial: Maintaining trials progress: Forms and data management, protocol deviations. Methods of data analysis: Binary responses, cross-over trials, survival data prognostic factors. Testing Hypothesis, Statistical Models: Inferential statistics-creating statistical hypothesis, the Z-test; designing a single variable experiment; errors in statistical decision making.  Power of test used in clinical trials/maximizing tests power. Significance testing:  t-test. Conducting two-way experiments and trials. Interpreting  overall results of Clinical Trials. Nonparametric Procedures/Tests & Ranked Data: , Mann-Whitney U test, Kruskal-Willis, Friedman.

 

 

Course Code: 
STA 809
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
STA 303
Select Programme(s): 
Statistics

TIME SERIES ANALYSIS

Stationary and non-stationary series: removal of trend and seasonality by differencing. Moments and auto-correlation. Models: simple AR and MA models (mainly AR(1), MA(1)): moments and auto-correlations; the conditions of stationarity: invertibility. Mixed (ARMA) models, and the AR representation of MA and ARMA models. Yule-Walker equations and partial auto-correlations (showing forms for simple AR, MA models). Examples showing simulated series from such processes, and sample auto-correlations and partial auto-correlations.  (Other models, e.g., trend and seasonal). Model identification: Elementary ideas of identification of models based on simple acf and pacf showing difficulties with real series. Estimation of parameter: initial estimate based on sample acf and pacf only (least squares estimates by iterative method). Result for standard error of sample acf, pacf and estimators. Forecasting: use of the AR representation for forecasting. Minimum mean square error forecasts. Updating.

 

Course Code: 
STA 815
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
STA 406
Select Programme(s): 
Statistics

ADVANCED TOPICS IN OPERATIONS RESEARCH

Formulating Linear Programming Models:  Goal programming, Transportation problem, Case study.  Mathematical Programming: Project planning and control, Dynamic programming,

Integer programming.  Probabilistic Models: Application of queuing theory, Forecasting and simulation, Decision analysis (making hard decisions), Multi-criteria decision making.

 

Course Code: 
STA 807
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
MAT409
Select Programme(s): 
Statistics

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