# MPhil Actuarial Science

Graduates’ skills can be applied in industry as Actuarial, Statistical, and high caliber Financial and Risk Analysts, just to mention a few. Such employment opportunities of the graduates of this programme will help in the design and operation good and viable National Health Insurance and Pension Schemes. The financial industry of Ghana will also benefit from the skills necessary for company strategic development and planning, financial product development, pricing and valuation of a wide variety of products in various sectors of the economy. In the academia, the programme also aims at providing a foundation for graduate studies in areas such as Actuarial Science, Statistics, Decision Science, Operations Research, Computational Finance and Risk Management, and Financial/Quantitative Finance who will in turn contribute to teaching and research in our tertiary institutions

**Aims and Objectives**

The MPhil degree programme in Actuarial Science seeks to develop individuals with a balance between mathematical, statistical, financial, and economic theories, and their applications to practical problems. The programme is designed to provide theoretical as well as applicable education in quantitative aspects of Risk Modelling and Management, Finance and Statistics. Graduates will be capable of abstracting mathematical models for real-world problems and applying appropriate computer-based solutions to them.

The graduates will also have the mathematical, statistical, and business skills needed to determine the expected costs and risks in any situation where there is financial uncertainty and data for creating a model for those unpredictable and unexpected contingencies (risks).

**Content of the Courses for each Semester**

**YEAR 1: SEMESTER 1**

**ACTS 561: FINANCIAL MATHEMATICS (3, 0, 3) **

Introduction to the mathematical theory of interest as well as the elements of economic and financial theory of interest. Topics include rates of interest and discount; simple, compound, real, nominal, effective, dollar (time)-weighted; present, current, future value; discount function; annuities; stocks and other financial instruments; definitions of key terms of modern financial analysis; yield curves; spot (forward) rates; duration; immunization; and short sales. The course will cover determining equivalent measures of interest; discounting; accumulating; determining yield rates; and amortization. Derivative pricing, fixed asset pricing, Neural networks, Valuing by expected utility.

**ACTS 563: RISK THEORY (3, 0, 3)**

This course covers the Statistical Methods that provide a further grounding in mathematical and statistical techniques of particular relevance to financial work. Topics include; Bayesian Statistics: Bayesian Theorem. Prior and Posterior distributions: Determining the posterior decisions, Continuous prior distributions, Conjugate prior, Improper prior distributions. The loss function: Quadratic loss, Absolute error loss, All – or – nothing loss, Some Bayesian posterior distributions. Loss Distributions: The exponential, gamma, normal, Pareto and generalised Pareto, lognormal, Weibull and Burr distributions. Estimation: The method of Moments and the maximum likelihood estimation of the exponential and gamma, the normal distribution, the Pareto and generalised Pareto, the lognormal and Weibull and Burr distributions. Goodness – of – fit test. Mixture distributions. Reinsurance: Proportional and Non – proportional reinsurance. Reinsurance arrangement: Excess of loss reinsurance – the insurer and the reinsurer. Proportional reinsurance. Particular distributions: Lognormal and normal distribution. Inflation. Estimations. Policy excess. Credibility theory: Credibility premium formula, the credibility factor. Bayesian credibility: Prior parameter distribution, likelihood function, Posterior distribution, loss function. The Poisson/gamma model with numerical illustration. The normal/normal model. The Bayesian approach to credibility. Empirical Bayes credibility theory: Model 1 and 2. Risk Model: Basic Risk Model. Collective Risk Model: Distribution functions and Convolutions. Compound Poisson, binomial and negative binomial distributions. Excess of loss insurance. Individual risk model. Ruin Theory: Surplus process, probability of ruin in continuous and discrete time process. Poisson and Compound Poisson. Probability of ruin in short term. The adjustment coefficient and Lundberg’s inequality and its application.

**ACTS 565: Survival and Stochastic Models (3,0,3) **

This course covers stochastic processes and survival models and their application. Topics include: Principles of actuarial modelling. **Stochastic processes**: Markov Chains, The two – state Markov Model, Time – homogeneous jump processes, Time – inhomogeneous Markov jump processes. **Survival Models**: Estimating the lifetime distributions, Proportional hazards models. The Binomial and Poisson models. Exposed to risk. Graduation and statistical tests. Methods of graduation.

**Prerequisite: **Calculus and probability

**ACTS 567: ACTUARIAL MATHEMATICS I (3,0,3)**

This course covers the mathematical and probabilistic structure of life contingent ﬁnancial instruments. It introduces survival models, covers life tables and their applications, life insurance, beneﬁts, lifetime annuities. Topics include; Probability Review, Survival Distributions: Probability functions, force mortality, mortality laws, moments, percentiles and recursions, fractional ages, selected mortality. Insurance: Continuous – Moments, annual and m-thly, moments, probabilities and percentiles, recursive formulas, varying insurances, relationships between Insurance payable at moment of death and payable at end of Year. Annuities: Continuous, Expectation, annual and m-thly, variance, probabilities and percentiles, varying annuities and recursive formulas, m-thly payments. Premiums: Net premiums for fully Continuous Insurances, net premiums for discrete insurances calculated from life tables, net premiums for discrete insurances calculated from formulas, net premiums paid on an m-thly basis, gross premiums, variance of future loss (Continuous), variance of future loss (discrete), probabilities and percentiles of future loss. Reserves: prospective benefit reserve.

**ACTS 569: Finance and Financial Reporting (3, 0, 3) **

This course covers a basic understanding of corporate finance including a knowledge of the instruments used by companies to raise finance and manage financial risk and to provide the ability to interpret the accounts and financial statements of companies and financial institutions. Topics include: **The key principle of finance**: Company ownership, Taxation, Financial instruments, Use of derivatives, Issue of shares. **Introduction to accounts: **The main accounts, Depreciation an reserves, Generating accounts, Group accounts and insurance company accounts, Interpretation of accounts, Limitations of accounts. Financial institutions. **Weighted average cost of capital**: Capital structure and dividend policy. Capital project appraisal.

**MATH 561: MEASURE AND INTEGRATION (3, 0, 3) **

Algebras, Measures, Construction of measures, Measurable functions, Construction of the integral, Integral for simple functions, Integral for positive measurable functions, Integral for measurable functions, Convergence theorems and applications, The three main convergence results, Consequences and applications, Lp-spaces, Minkowski and Holder's inequalities, Completeness of Lp, Lp-spaces on intervals, Applications to Fourier series Introduction of Fourier Series, Fourier coefficients, Fourier series in , Fourier series.

**Year 1 Semester 2**

**ACTS 562: FINANCIAL ECONOMICS (4, 0, 4) **

The course covers asset-liability models and to how value financial derivatives. These skills are also required to communicate with other financial professionals and to critically evaluate modern financial theories. Topics include: The efficient markets hypothesis, Utility theory and stochastic dominance. Measurement of investment risk. Portfolio theory. Models of asset returns. Asset pricing Models. Brownian motion and Martingales. Stochastic calculus and Ito processes. Interest rate models: Vasicek and Cox-Ingersoll-Ross bond price models, Black-Derman-Toy model binomial model matching in a given time zero yield curve and a set of volatilities:Rational Valuation of Derivative securities: Use put-call parity to determine the relationship between prices of European put and call options and to identify arbitrage opportunities. Computation of European and American options using Binomial and Black-Scholes option-pricing models, Calculation and interpretation of option Greeks, Cash flow characteristic of exotic options; Asian, Barrier, Compound, Gap and Exchange, Stock prices and Diffusion Process, Ito’s Lemma in one dimensional case and Option pricing concepts to Actuarial problems such as equity-linked insurance, Risk Management Techniques: Control of risk using the method of delta-hedging. Credit Risk.

**ACTS 564: Statistical Modelling (3, 0, 3)**

This course covers the Statistical Methods that provide a further grounding in mathematical and statistical techniques of particular relevance to financial work. Topics include; **Decision Theory**: zero – sum two player games-domination, the minimax criterion-saddle points, and Randomized strategies. Statistical games. Decision criteria: the minimax criterion, the Bayes criterion. **Generalized linear Models: **Exponential families: normal, Poisson and binomial distributions. Link functions and linear predictors, Deviance of model fitting. **Run – off triangles**: Estimating future claims. Projection using development factors. Chain – ladder method. The inflation adjusted chain ladder. The Bornhuetter – Fergusson Method. **Time series**. **Monte Carlo simulation**.

**ACTS 566: Economics for Actuaries (3, 0, 3) **

This course covers fundamental concepts of micro and macroeconomics as they affect the operation of insurance and other financial systems. Topics include: **Economics concepts: **Demand and supply, Elasticity and uncertainty, Consumer demand and uncertainty, Production and costs, Revenue and profit. **Perfect competition and monopoly: **Imperfect competition, Products, marketing and advertising, Growth strategy, Pricing strategies. **Government intervention in markets:** Government and the firm. Supply – side policy. International trade. The balance of payments and exchange rates. The macroeconomic environment. Money and interest rates. Business activity, unemployment and inflation. Demand – side macroeconomic policy.

**ACTS 568: ACTUARIAL MATHEMATICS II (3,0,3)**

Decrements modeling and their applications to insurance and annuities, non-stochastic interest rate models to calculate present values and annuities. Models for cash flows and non-interest sensitive insurances other than traditional life insurances and annuities. Models for contract cash flows for basic universal life insurances. Models for cash flows of basic universal life insurance. Calculate the benefit reserve. Models that consider expense cash flows. Calculate an expense factor using the appropriate exposure. Calculate probabilities and moments of the present-value-of-expenses random variable based on single decrement on single life model and multiple decrements on a single life models. Modeling of expense reserve. Calculate a gross premium given expenses and benefits based on: the equivalence principle; and a return on gross profits basis. Modeling gross premium reserve. Modeling of asset share. Severity Models: compute the basic distributional quantities such as moments, percentiles, generating functions: Frequency Models, Aggregate Models: compute relevant parameters and statistics for collective risk models, evaluate compound models for aggregate claims, compute aggregate claims distributions.

**ACTS 572: Investment and Asset and Liabilities Management (ALM) for Actuaries (3, 0, 3) **

This course develops an understanding of the fundamental concepts of Investment and Asset Liability Management (ALM) for actuaries. A basic knowledge of financial mathematics is assumed. This course is an elective course, which provides students with the knowledge to apply in a practical sense the theoretical framework that they learned from the foundational actuarial examinations. Topics to be considered are Investment and valuation, general principles of asset allocation, Investment risk, Portfolio selection techniques and Investment modeling, asset and liability modeling.

**ACTS 574: PENSION MATHEMATICS (3, 0, 3)**

This course focuses on fundamental issues of pension mathematics. The course content focuses on pensions system in Ghana, pension mathematics and investment of pension fund. Topics include: Introduction of pension systems in Ghana and pension plan benefits. Objectives of pension mathematics and fundamental structure. Actuarial assumptions which include decrement assumptions, salary assumptions and interest rate assumptions. General theory for funding method. Funding method used for actual pension management. Practical actuarial valuation to check appropriateness of actuarial assumptions.

**ACTS 578: Predictive Analytics (3, 0, 3)**

Predictive Analytics Problems and Tools, Problem definition, Data Visualization, Data Types and Exploration, Data Issues and Resolution, Generalized Linear Models, Decision Trees, Cluster and Principal Component Analysis, Communication.

**ACTS 580: ****General Insurance Reserving and Capital Modelling Principles (3, 0, 3) **

**General insurance products and general business environment**: types of general insurance for customer needs, the financial and other risks they pose for the general insurer including their capital requirements and possible effect on solvency. the main features of the general insurance market, the effect of different marketing strategies, fiscal regimes, inflation and economic factors, legal, political and social factors, professional guidance and the impact of technological change. **Risk, uncertainty and regulation**: the major areas of risk and uncertainty in general insurance business with respect to reserving and capital modelling, in particular those that might threaten profitability or solvency. Purposes of regulating general insurance business. **Reserving**: with regard to reserving work using triangulations, appropriate reserving bases for general insurance business, stochastic reserving processes. **Capital modelling**: Evaluate the following approaches to capital modelling; deterministic models, stochastic model. Assess capital requirements for the following risk types; insurance, market, credit, operational, liquidity and group risk. **Data, investigations, reinsurance and accounting**: With regard to the use of data in reserving and capital modelling, the principles of investment, the asset liability matching requirements of a general insurer, develop an appropriate investment. Strategy, the methods and principles of accounting for general insurance business and interpret the accounts of a general insurer, the changes to accounting methods expected under IFRS.