## DEPARTMENT OF STATISTICS AT UNIVERSITY OF GHANA

COURSE DESCRIPTIONS

ACTUARIAL SCIENCE

ACTU 101: Introduction to Statistics and Probability for Actuaries

To introduce students to basic concepts in Statistical Methods and Probability. Topics include

introduction to Statistics: The interpretation of data. Types of data. Methods of data

transformation: Graphical display of data, numerical characterization of data. Univariate and

bivariate exploratory data analysis. Introduction to basic concepts of Probability. Random events,

and Random Variables. The Probability Calculus and some univariate probability distributions.

Some applications to Actuarial Science.

LEVEL 200, 300 and 400 COURSES

ACTU 202: Data Analysis and Statistical Computing

To acquaint students with elementary modern computing methods appropriate to the work of an

actuary. This course is largely practical and involves analyzing large data sets. Students will be

introduced to modeling and statistical simulations using modern statistical software such as R.

Exploratory Data Analysis and Confirmatory Data Analysis of both univariate and bivariate cases

will be explored. Applications will be tailored to meet requirements of the Actuarial profession

with hands-on training sessions with large data sets. No ‘new’ statistical methods should be

presented but interesting data can be analyzed using known methods on the chosen package.

Topics should include graphics, descriptive statistics, representations of multivariate data, simple

hypothesis tests, analysis of variance, and linear regression.

ACTU 320: Internship in Actuarial Science

Aim: The core aim of this course is to introduce students to the Actuarial practices in jobs that

they find themselves in. This in turn will bridge the gap between theory and practice. The course is

offered in both semesters to students to seek practical applications of actuarial principles in

insurance companies, financial institutions, pension consulting firms, and other related fields. The

course requires students to participate in an internship program within the industry. Students need

to submit monthly progress reports and a final semester report to the Head, Department of

Statistics, University of Ghana, Legon.

ACTU 303: Introduction to Financial Mathematics

To provide grounding in Financial Mathematics and its simple applications. Topics to be

introduced include: Time value of money. Simple and Compound Interest accumulation and

discount functions. Theoretical continuous cases of forces of interest and discount, effective rates

of interest and discount and present values, as applied to annuities and other financial products,

and applications including the determination of loan repayment once interest rate assumptions

have been made.

ACTU 304: Life Contingencies

To help students to know the fundamental techniques relevant to the valuation of cash flows which

are a function of death, survival and other uncertain risks. Models that depict time until death,

analysis of probability distributions and present values associated with multiple decrement and

multiple life models. Application of probability to problems of life and death. The determination

of premiums for insurances and annuities in discrete and continuous cases. Single life annuity and

life insurance loss random variables and their probability distributions with application to analysis

of benefits, premiums, net premiums and net premium reserves. Mortality table, measures of

mortality, force of mortality graduation. The identity of the forces.

ACTU 403: Elements of Life Insurance

To instill the ability, in simple situations, to use judgment and apply the principles of actuarial

planning and control needed for the operation on sound financial lines of providers of life

insurance. Principal terms; The main contract types; The principles of life insurance markets; Data

requirements and verification; Product pricing; Reserving; Surrender values; Policy alterations;

Derivation of actuarial assumptions; Measurement and analysis of surplus; Methods of distributing

surplus to policyholders; Principles of investment and asset-liability modeling; Principles of

regulation and accounting; Risk and uncertainty in life insurance business; Principles of risk

management including reinsurance; Life insurance regulations, including: Taxation, Accounting,

Supervisory regulation; Experience rating; Future financial requirements including dynamic

financial analysis; Value of a life company; Evaluation of the capital requirements of a life insurer

for the purpose of determining the strategy for growth in business.

ACTU 404: Pensions and Social Security

To make students aware of the environment of effective social security system and pension and

employee benefit schemes. The theory and practice of social security and state, occupational and

personal pension plan funding. Features of the main employee benefit schemes, principles of

financing, including asset and liability relationships. Legislative framework on retirement and

various benefit schemes. Tax management, economic and demographic factors, accounting for

pension cots, valuation data collection, analysing experience, valuing liabilities and assets,

calculating contribution rates; choice and management of assets.

474

ACTU 407: Survival Analysis and Modelling

To provide understanding of survival analyses and how to model concepts in practice in order to

fix a trail for information. Topics that students will be exposed to include: Survival models,

estimation of survival function and hazard function, estimation and fitting of survival model,

parametric survival model, determining the optional parameters. Models for loss severity:

parametric models, models for loss frequency, mixed Poisson models, compound Poisson models.

Aggregate claims models, Classical ruin theory.

ACTU 409: Introduction to Actuarial Mathematics

To provide introductory preparation in Actuarial mathematics and their applications. Deterministic

theory of interest (i.e. traditional compound interest, cash-flow modelling; annuities certain, bond

market theory), Introduction to contingent claims analysis (i.e. definition of derivative securities,

no arbitrage principle); Stochastic calculus for finance (conditional expectation, introduction to

martingales, stochastic integrals and differential equations, pricing and hedging of derivatives);

Stochastic theory of interest; interest rate models (discrete and continuous time); derivatives on

interest rates and bonds; Dynamic portfolio management (asset-liability modeling; introduction to

stochastic optimal control); Introductory applications to insurance liabilities (embedded options in

life insurance; valuation techniques for embedded options)

STATISTICS

STAT 111: Introduction to Statistics

Introduction to Statistics. The reduction and interpretation of data.

STAT 112: Elementary Probability

Introduction to basic concepts of Probability, Random event and Random ariables.

Probability Calculus and some univariate probability distributions.

STAT 221: Introductory Probability I (Pre-req. MATH 121, 122)

Introduction to the concepts of probability, Random Events, and Random Variables. The

Probability Calculus, Univariate probability distributions.

STAT 222: Data Analysis I (Pre-Req. STAT 223)

The aim of this course is to give students practice in handling large data Sets; specifically to

provide opportunities for Descriptive and Exploratory Studies.

STAT 223: Elementary Statistical Methods

Bivariate Data Analysis. Time Series and Elements of statistical inference.

STAT 224: Introductory Probability II (Pre-Req. STAT 221)

Bivariate Distribut ions. Moment Gener at ing Funct ions; the i r properties and uses.

Sampling distributions. Distributions associated with samples from a Normal population. The

Weak Law of Large Numbers and the Central Limit Theorem. Applications.

STAT 226: Official Statistics

Purposes and Scope of Official Statistics. Structure and Work of the National Statistical System.

Organisational, Methods and Practices of data collection and dissemination.

475

STAT 331: Probability Distributions (Pre-req. STAT 221, 224)

Elementary Distribution Theory. Generating Functions. Sequences of random variables;

the Central Limit Theorem and its applications.

STAT 332: Multivariate Distributions (Pre-req. STAT 331)

Introduction to Vector Random Variables. Distribution Concepts for Several random variables.

Transformations of random vectors. Order Statistics. The multivariate Normal Distribution.

STAT 333: Statistical Methods I (Pre-req. STAT 224)

The first part of a two-semester Course providing a systematic development of the principles and

methods of statistical inference, on a largely intuitive basis, with a minimum of mathematical

theory. This part deals with the general nature of Statistical Problems, Statistical Models and

Problems of Estimation.

STAT 334: Statistical Methods II (Pre-req. STAT 333)

Sequel to STAT 333. General Principles and Procedures of Hypothesis Testing. Parametric and

Non-parametric Tests. Simple Linear Regression and Correlation Analysis. The Analysis of

Frequency Data.

STAT 335: Sample Survey Methods

Basic Sample Survey procedures and Sample Designs. Estimation of population parameters.

Sampling and Non-Sampling Errors.

STAT 336: Design of Experiments (Pre-req. STAT 223)

Basic concepts and principles of experimental Statistics. Analysis of Variance for standard

experimental designs. The estimation of treatment Effects.

STAT 440: Data Analysis II (Pre-req. STAT 222, 233)

Summary Statistics for Multivariate Data. Data Presentation and Report Writing. Random Sample

Selection. Discrete Analysis. Fitting and Testing Probability Models. Regression and Curve

Fitting. Analysis of Experimental Data.

STAT 441: Statistical Inference: Estimation (Pre-req. STAT 331, 333)

The Theoretical basis of the methods of Point and Interval Estimation. Uniformly Minimum

Variance Unbiased (UMVU) Estimation, and Maximum Likelihood Estimation.

STAT 442: Statistical Inference: Tests of Hypotheses (Pre-req. STAT 331, 334)

The Theory of Hypothesis Testing. Optimal tests. Uniformly Most Powerful Test. Likelihood

Ratio and related procedures.

STAT 443: Theory of Sampling (Pre-req. STAT 224)

Analysis and comparison of various sampling schemes. Optimal designs.

STAT 444: Survey Organization and Management (Pre-req. STAT 335)

Multi-subject and specialized Socio-Economic Surveys. Household Survey. Planning, Design and

Organization. Error Co n t ro l . Problems relat ing to Concepts, De f ini t ions ,

Cla s s i f ica t io n a nd Measurement.

476

STAT 445: Regression Analysis (Pre-req. STAT 334)

The methods of regression analysis extended to situations involving more than one predictor

variable. Special emphasis on problems associated with the presence of several predictors.

STAT 446: Multivariate Methods (Pre-req. STAT 332)

Introduction to theory and methods of Multivariate Data Analysis; Estimation and Tests of

Hypotheses, Profile Analysis, Multivariate Structure, Discriminant Analysis.

STAT 447: Non-Parametric Statistics (Pre-req. STAT 333, 304)

Some Single Sample problems; the problem of location, The Sign Test, The Wilcoxon Signed

Ranks test. Some Two-Sample Problems: The Chi-Square Test for Homogeneity, the Median

Test, the Mann-Whitney-Wilcoxon Test. Chi-Square Tests of Independence. Some Users of Order

Statistics Distributions under alternative Hypotheses.

STAT 448: Analysis of Experimental Designs (Pre-req. STAT 336)

Model specialization for single-factor and multi-factor designs. Main effects, specific effects and

interactions. Estimation. Multiple Comparisons. Analysis of covariance.

STAT 450: Project

This is a yearlong project. Student presents a project on a topical issue in Statistics using tools

acquired over the period to solve statistical problems.

STAT 451: Introduction to Stochastic Processes (Pre-req. STAT 331)

Stochastic models in the natural and social sciences. Some discrete and continuous time processes.

Basic theory and Applications.

STAT 453: Population Statistics

Demographic Concepts and Measures. Collection and Evaluation of demographic data. Analysis

of Demographic data. The Dynamics of Population change.

STAT 454: Biometrics (Pre-req. STAT 331)

Biological assay, Analysis of quantal responses. Agricultural and Clinical Trials. Sampling and

Estimation of Biological Populations.

STAT 455: Actuarial Statistics I (Financial Statistics) (Pre-req. STAT 331)

Principles of time value of money. Concepts of Compound Interest and Discounting. Interest or

Discount Rates. Compound Interest Functions. Investment Projects appraisals. Stochastic Interest

Rate Models.

STAT 456 : Actuarial Statistics II (Pre-req. STAT 455, Recommended STAT 453) Principles

of simple life insurance and annuity contracts. Means and variances of payment under these

contracts. Determination of expected present value and variances of benefits. Determination of

net premiums and net premium policy values. Survival models.

STAT 457: Economic and Social Statistics I (Pre-req. STAT 226)

Statistics on Economic and Social Activities and Trends, and their uses. Methods and Sources of

Data Collection. Indices and Indicators of Economic Activity. Indicators of Social Development

and Living Standard.

STAT 458: Economic and Social Statistics II (Pre-req. STAT 447)

Introduction to the System of National Accounts (SNA). The System, its Accounts and their

corresponding economic activities. Input-Output Tables. Social Accounting. Corresponding

economic activities. Input-Output Tables. Social Accounting.