Actuarial Mathematics BSc (Hons)
 Course length: 3 years
 UCAS code: NG31
 Year of entry: 2018
 Typical offer: Alevel : AAB / IB : 35 / BTEC : Applications considered
Honours Select
×This programme offers Honours Select combinations.
Honours Select 100
×This programme is available through Honours Select as a Single Honours (100%).
Honours Select 75
×This programme is available through Honours Select as a Major (75%).
Honours Select 50
×This programme is available through Honours Select as a Joint Honours (50%).
Honours Select 25
×This programme is available through Honours Select as a Minor (25%).
Study abroad
×This programme offers study abroad opportunities.
Year in China
×This programme offers the opportunity to spend a Year in China.
Accredited
×This programme is accredited.
Module details
Programme Year One
The Actuarial Maths degree has been accredited by the UK Actuarial Profession, which means that students can obtain exemption from some of the subjects in the Institute and Faculty of Actuaries’ examination system.
All exemptions will be recommended on a subjectbysubject basis, taking into account performance at the University of Liverpool.
Further information can be found at the actuarial profession’s website.
Core Technical Stage
Exemptions are based on performance in the relevant subjects as listed below.
Subject CT1 Financial Mathematics: Financial Mathematics I &II
Subject CT2 Finance & Financial Reporting: Introduction to Financial Accounting, Introduction to Finance & Financial Reposting and Finance
Subject CT3 Probability & Mathematical Statistics: Statistical Theory I & II
Subject CT4 Models: Applied Probability & Actuarial Models
Subject CT5 Contingencies: Life Insurance Mathematics I & Life Insurance Mathematics II
Subject CT6 Statistical Methods: Mathematical Risk Theory & Statistical Methods in Actuarial Science
Subject CT7 Economics: Principles of Microeconomics, Principles of Macroeconomics, Microeconomics I & International Trade.
Subject CT8 Financial Economics: Financial Mathematics II, Security Markets & Stochastic Modelling in Insurance and Finance
Year One Compulsory Modules
Introduction to Financial Accounting (ACFI101)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 70:30 Aims To develop knowledge and understanding of the underlying principles and concepts relating to financial accounting and technical proficiency in the use of double entry accounting techniques in recording transactions, adjusting financial records and preparing basic financial statements.
Learning Outcomes Prepare basic financial statements
Explain the context and purpose of financial reporting
Demonstrate the use of double entry and accounting systems
Record transactions and events
Prepare a trial balance
Calculus I (MATH101)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims 1. To introduce the basic ideas of differential and integral calculus, to develop the basic skills required to work with them and to apply these skills to a range of problems.
2. To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.
3. To introduce the notions of sequences and series and of their convergence.
Learning Outcomes differentiate and integrate a wide range of functions;
sketch graphs and solve problems involving optimisation and mensuration
understand the notions of sequence and series and apply a range of tests to determine if a series is convergent
Calculus II (MATH102)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims · To discuss local behaviour of functions using Taylor’s theorem.
· To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.
Learning Outcomes use Taylor series to obtain local approximations to functions;
obtain partial derivaties and use them in several applications such as, error analysis, stationary points change of variables
evaluate double integrals using Cartesian and Polar Coordinates
Introduction to Linear Algebra (MATH103)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims  To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
 To develop geometrical intuition in 2 and 3 dimensions.
 To introduce students to the concept of subspace in a concrete situation.
 To provide a foundation for the study of linear problems both within mathematics and in other subjects.
Learning Outcomes manipulate complex numbers and solve simple equations involving them
solve arbitrary systems of linear equations
understand and use matrix arithmetic, including the computation of matrix inverses
compute and use determinants
understand and use vector methods in the geometry of 2 and 3 dimensions
calculate eigenvalues and eigenvectors and, if time permits, apply these calculations to the geometry of conics and quadrics
Introduction to Statistics (MATH162)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 Aims To introduce topics in Statistics and to describe and discuss basic statistical methods.
To describe the scope of the application of these methods.
Learning Outcomes to describe statistical data;
to use the Binomial, Poisson, Exponential and Normal distributions;
to perform simple goodnessoffit tests
to use the package Minitab to present data, and to make statistical analysis
Principles of Microeconomics (ECON121)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 80:20 Aims This module aims to provide students with a clear foundation of the purpose, scope and topics of microeconomic analysis. Students will develop their ability to think critically and analytically, and understand how to frame real world problems in an economic model. This module forms the starting point for all future courses in Microeconomics.
This module also emphasizes the role of mathematics in economics.
Learning Outcomes Students will have the ability to understand, explain, analyse and solve core problems in microeconomics.
Students will be able to practice and develop their mathematical techniques and understand the role of mathematical analysis in Microeconomics.
Students will be able to familiarise themselves with the principles of using an ''economic model'' and how to model individual decisionmaking for both consumers and producers.
Students will be able to apply their understanding of economic decisionmaking, optimisation and equilibrium to real world situations.
Principles of Macroeconomics (ECON123)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 40:60 Aims The aims of this module are:
 To complement and build on Principles of Microeconomics and to provide a foundation for further studies in macroeconomics
 To introduce concepts and theories of economics which help understand changes in the macroeconomic environment
 to explain and analyse the formulation of government macroeconomic policy
Learning Outcomes · Explainthe relationship between expenditures and national income and demonstrate howmonetary and fiscal policies may be used to influence them
· Explainthe behaviour of economic aggregates such as national income, inflation andunemployment over time
· Explainand assess government policy in a range of policy situations
· Explainthe framework of national income accounting
· Usegraphical and algebraic modelling to analyse the economy and economic policy
· Explainthe interconnections between the markets for goods, money and labour
· Explainthe principal influences on longterm growth and the shortrun fluctuation inoutput around the longrun growth trend
· Locate,select and analyse information relevant to assessing the state of the economyand economic policy
Introduction to Finance (ACFI103)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims to introduce the students to finance.
 to provide a firm foundation for the students to build on later on in the second and third years of their programmes, by covering basic logical and rational analytical tools that underpin financial decisions
Learning Outcomes Understand the goals and governance of the firm, how financial markets work and appreciate the importance of finance.
Understand the time value of money
Understandthe determinants of bond yields
Recognizehow stock prices depend on future dividends and value stock prices
Understandnet present value rule and other criteria used to make investment decisions
Understand risk, return and the opportunity cost of capital
Understandthe riskreturn tradeoff, and know the various ways in which capital can beraised and determine a firm''s overall cost of capital
Knowdifferent types of options, and understand how options are priced
Programme Year Two
In the second and subsequent years of study, there is a wide range of modules. Each year you will choose the equivalent of eight modules. Please note that we regularly review our teaching so the choice of modules may change.
Please note that along with the compulsory module, two modules in Life Insurance and Financial Reporting & Finance must be taken.
Year Two Compulsory Modules
Financial Reporting and Finance (nonspecialist) (ACFI290)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims The aim of the Financial Reporting and Finance module is to provide an understanding of financial instruments and financial institutions and to provide the ability to interpret published financial statements of nonfinancial and financial companies with respect to performance, liquidity and efficiency. An understanding of the concepts of taxation and managerial decision making are also introduced and developed.
Learning Outcomes Describe the different forms a business may operate in; Describe the principal forms of raising finance for a business;
Demonstrate an understanding of key accounting concepts, group accounting and analysis of financial statements;
Describe the basic principles of personal and corporate taxation;
Demonstrate an understanding of decision making tools in used in management accounting.
Microeconomics 1 (ECON221)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 70:30 Aims This module, in accordance with Microeconomics 2, aims to provide a solid foundation of intermediate level microeconomic theory. It develops and extends three of the topics introduced in Principles of Microeconomics, namely, Consumer Theory, Producer Theory and General Equilibrium. It prepares the students for the more advanced modules in the second and third year like Microeconomics 2 and Game Theory.
Learning Outcomes Students will be able to demonstrate a thorough understanding of the core concepts and models used in consumer theory, producer theory and general equilibrium and an ability to apply these to arange of markets and settings. Students will be able to think and apply themselves analytically to problems in the abovementioned topics.
Students will be able to gain problem solving skills using verbal, diagrammatic and mathematical methods to problems in the above topics.
Students will be able to have a critical perspective regarding the assumptions underlying microeconomics models.
Financial Mathematics I (MATH267)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims This module is to provide an understanding of the fundamental concepts of financial mathematics, and how these concepts are applied in calculating present and accumulated values for various streams of cash flows. Students will also be given an introduction to financial instruments, such as derivatives, the concept of noarbitrage.
Learning Outcomes 1. Understand and calculate all kind of rates of interest, find the future value and present value of a cash flow, and write the equation of value given a set of cash flows and an interest rate.
2. Derive formulae for all kinds of annuities
3. Given an annuity with level payments, immediate (or due) , payable mthly, (or payable continuously), and any three of present value, future value, interest rate, payment, and term of annuity, calculate the remaining two items.
4. Given an annuity with nonlevel payments, immediate (or due) , payable mthly, (or payable continuously), the pattern of payment amounts, and any three of present value, future value, interest rate, payment, and term of annuity, calculate the remaining two items.
5. Calculate the outstanding balance at any point in time.
6. Calculate a schedule of repayments under a loan and identify the interest and capital components in a given payment.
7. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.
8. Calculate the present value of payments from a fixed interest security, bounds for the present value of a redeemable fixed interest security.
9. Given the price, calculate the running yield and redemption yield from a fixed interest security.
10. Calculate the present value or real yield from an indexlinked bond.
11. Calculate the price of, or yield from, a fixed interest security where the income tax and capital gains tax are implemented.
12. Calculate yield rate, the dollarweighted and time weighted rate of return, the duration and convexity of a set of cash flows.
13. Describe the concept of a stochastic interest rate model and the fundamental distinction between this and a deterministic model.
Life Insurance Mathematics I (MATH273)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims Provide a solid grounding in the subject of life contingencies for single life, and in the subject of the analysis of life assurance and life annuities, including pension contracts.
Provide an introduction to mathematical methods for managing the risk in life insurance,?Develop skills of calculating the premium for a certain life insurance contract, including allowance for expenses and profits?Prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CT5 subject of the Institute and Faculty of Actuaries.
Learning Outcomes Be able to explain and analyze the factors that affect mortality, simple life assurance and life annuity contracts.
Understand the concept (and the mathematical assumptions) of the future life time random variables in continuous and discrete time,Be able to define the survivals probabilities and the force of mortality of the (c) section of the Syllabus, explain these types of probabilities and the force of mortality intuitively, be able to calculate the different types of the survival probabilities in theoretical and numerical examples.
Understand the concept of the De Moivre, Makeham, Gompertz, Weibull and the exponential law (constant force of mortality) for modelling fractional ages, explain the basic difference between the laws above, be able to use these laws to calculate the survival probabilities of (c) of the Syllabus in numerical examples.
Understand, define/calculate and derive the expected present values of all types of the life assurances of (d) of the Syllabus. Derive relations between life assurances both in continuous and discrete time, be able to use recursive equations for the calculation of the expected present value of different types of life assurances, calculate the variance of the present values for basic forms of life assurances.
Be able to derive the distributions and the moment/variance of the aforementioned future lifetimes, be able to make graphs of these future life times.
Securities Markets (ECON241)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims This module seeks to provide an understanding of
the role of securities markets in the economy
their basic mechanics and technical features
the valuation of financial assets
the operational and allocative efficiency of the market.
Learning Outcomes appreciate the central role of securities markets in the economy. understand and apply appropriate economic theory to market organisation
display an understanding of the usefulness of portfolio theory and the approaches to the valuation of financial assets.
read the financial press and appreciate issues relating to the study of the securities markets.
Financial Mathematics II (MATH262)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims to provide an understanding of the basic financial mathematics theory used in the study process of actuarial/financial interest,
to provide an introduction to financial methods and derivative pricing financial instruments ,
to understand some financial models with applications to financial/insurance industry,
to prepare the students adequately and to develop their skills in order to be ready to sit for the CT1 & CT8 subject of the Institute of Actuaries (covers 20% of CT1 and material of CT8).
Learning Outcomes After completing the module students should:
(a) Understand the assumptions of CAMP, explain the no riskless lending or borrowing and other lending and borrowing assumptions, be able to use the formulas of CAMP, be able to derive the capital market line and security market line,
(b) Describe the Arbitrage Theory Model (APT) and explain its assumptions, perform estimating and testing in APT,
(c) Be able to explain the terms long/short position, spot/delivery/forward price, understand the use of future contracts, describe what a call/put option (European/American) is and be able to makes graphs and explain their payouts, describe the hedging for reducing the exposure to risk, be able to explain arbitrage, understand the mechanism of short sales,
(d) Explain/describe what arbitrage is, and also the risk neutral probability measure, explain/describe and be able to use (perform calculation) the binomial tree for European and American style options,
(e) Understand the probabilistic interpretation and the basic concept of the random walk of asset pricing,
(f) Understand the concepts of replication, hedging, and delta hedging in continuous time,
(g) Be able to use Ito''s formula, derive/use the the Black‐Scholes formula, price contingent claims (in particular European/American style options and forward contracts), be able to explain the properties of the Black‐Scholes formula, be able to use the Normal distribution function in numerical examples of pricing,
(h) Understand the role of Greeks , describe intuitively what Delta, Theta, Gamma is, and be able to calculate them in numerical examples.
Statistical Theory and Methods I (MATH263)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 85:15 Aims To introduce statistical methods with a strong emphasis on applying standard statistical techniques appropriately and with clear interpretation. The emphasis is on applications.
Learning Outcomes After completing the module students should have a conceptual and practical understanding of a range of commonly applied statistical procedures. They should have also developed some familiarity with the statistical package MINITAB.
Statistical Theory and Methods II (MATH264)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims To introduce statistical distribution theory which forms the basis for all applications of statistics, and for further statistical theory.
Learning Outcomes After completing the module students should understand basic probability calculus. They should be familiar with a range of techniques for solving real life problems of the probabilistic nature.
Year Two Optional Modules
Ordinary Differential Equations (MATH201)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations.
To illustrate the breadth of applications of ODEs and fundamental importance of related concepts.
Learning Outcomes After completing the module students should be:
 familiar with elementary techniques for the solution of ODE''s, and the idea of reducing a complex ODE to a simpler one;
 familiar with basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions;
 well versed in the solution of linear ODE systems (homogeneous and nonhomogeneous) with constant coefficients matrix;
 aware of a range of applications of ODE.
Mathematical It Skills (MATH111)
Level 1 Credit level 15 Semester First Semester Exam:Coursework weighting 0:100 Aims To acquire key mathematicsspecific computer skills.
To reinforce mathematics as a practical discipline by active experience and experimentation, using the computer as a tool.
To illustrate and amplify mathematical concepts and techniques.
To initiate and develop modelling skills.
To initiate and develop problem solving, group work and report writing skills.

To develop employability skills
Learning Outcomes After completing the module, students should be able to
 tackle project work, including writing up of reports detailing their solutions to problems;
 use computers to create documents containing formulae, tables, plots and references;
 use MAPLE to manipulate mathematical expressions and to solve simple problems,
 better understand the mathematical topics covered, through direct experimentation with the computer.
After completing the module, students should be able to
 list skills required by recruiters of graduates in mathematical sciences;
 recognise what constitutes evidence for those skills;
 identify their own skills gaps and plan to develop their skills.
Mathematical Models: Microeconomics and Population Dynamics (MATH227)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims 1. To provide an understanding of the techniques used in constructing, analysing, evaluating and interpreting mathematical models.
2. To do this in the context of two nonphysical applications, namely microeconomics and population dynamics.
3. To use and develop mathematical skills introduced in Year 1  particularly the calculus of functions of several variables and elementary differential equations.
Learning Outcomes After completing the module students should be able to:
 Use techniques from several variable calculus in tackling problems in microeconomics.
 Use techniques from elementary differential equations in tackling problems in population dynamics.
 Apply mathematical modelling methodology in these subject areas.
All learning outcomes are assessed by both examination and course work.
Introduction to Methods of Operational Research (MATH261)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 Aims  Appreciate the operational research approach.
 Be able to apply standard methods to a wide range of realworld problems as well as applications in other areas of mathematics.
 Appreciate the advantages and disadvantages of particular methods.
 Be able to derive methods and modify them to model realworld problems.
 Understand and be able to derive and apply the methods of sensitivity analysis.
Learning Outcomes Appreciate the operational research approach.Be able to apply standard methods to a wide range of realworld problems as well asapplications in other areas of mathematics.
Appreciate the advantages and disadvantages of particular methods.
Be able to derive methods and modify them to model realworld problems.Understand and be able to derive and apply the methods of sensitivity analysis. Appreciate the importance of sensitivity analysis.
Microeconomics 1 (ECON221)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 70:30 Aims This module, in accordance with Microeconomics 2, aims to provide a solid foundation of intermediate level microeconomic theory. It develops and extends three of the topics introduced in Principles of Microeconomics, namely, Consumer Theory, Producer Theory and General Equilibrium. It prepares the students for the more advanced modules in the second and third year like Microeconomics 2 and Game Theory.
Learning Outcomes Students will be able to demonstrate a thorough understanding of the core concepts and models used in consumer theory, producer theory and general equilibrium and an ability to apply these to arange of markets and settings. Students will be able to think and apply themselves analytically to problems in the abovementioned topics.
Students will be able to gain problem solving skills using verbal, diagrammatic and mathematical methods to problems in the above topics.
Students will be able to have a critical perspective regarding the assumptions underlying microeconomics models.
Introduction to the Methods of Applied Mathematics (MATH224)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics.
To introduce some of the basic tools (Fourier Series) used in the solution of differential equations and other applications of mathematics.
Learning Outcomes After completing the module students should:
 be fluent in the solution of basic ordinary differential equations, including systems of first order equations;
 be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations;
 be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations;
 be able to solve simple first order partial differential equations;
 be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.
Measure Theory and Probability (MATH265)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims The main aim is to provide a sufficiently deep introduction to the measure theory and to the Lebesgue theory of integration. In particular, this module aims to provide a solid background for the modern probability theory which is essential for Financial Mathematics.
Learning Outcomes After completing the module students should be able to:
· master the basic results about measures, measurable functions, Lebesgue integrals and their properties;
· to understand deeply the rigorous foundations of the probability theory;
· to know certain applications of the measure theory to probability and financial mathematics.
Numerical Methods (MATH266)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 Aims To provide an introduction to the main topics in Numerical Analysis and their relation to other branches of Mathematics
Learning Outcomes After completing the module students should be able to:
• write simple mathematical computer programs in Maple,
• understand the consequences of using fixedprecision arithmetic,
• analyse the efficiency and convergence rate of simple numerical methods,
• develop and implement algorithms for solving nonlinear equations,
• develop quadrature methods for numerical integration,
• apply numerical methods to solve systems of linear equations and to calculate eigenvalues and eigenvectors,
• solve boundary and initial value problems using finite difference methods.
Microeconomics 2 (ECON222)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 70:30 Aims This module, following on from with Microeconomics 1, aims to provide a solid foundation of intermediate level microeconomic theory.
The module uses the theoretical foundations developed in the first semester and aims to extend the application of the skills acquired to more advanced topics such as welfare economics.
This module also aims to prepare students for the more advanced modules in the third year by introducing topics such as asymmetric information and game theory.
Learning Outcomes Have a thorough understanding of the core concepts and models used in Welfare Economics, Asymmetric Information, and Game Theory. To prepare students to think and apply themselves to analyse a range of problems in the three areas mentioned above.
To develop problem solving skills using verbal, diagrammatic and mathematical methods to problems in the above topics.
To deepen a critical perspective regarding the assumptions underlying microeconomics models.
Securities Markets (ECON241)
Level 2 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims This module seeks to provide an understanding of
the role of securities markets in the economy
their basic mechanics and technical features
the valuation of financial assets
the operational and allocative efficiency of the market.
Learning Outcomes appreciate the central role of securities markets in the economy. understand and apply appropriate economic theory to market organisation
display an understanding of the usefulness of portfolio theory and the approaches to the valuation of financial assets.
read the financial press and appreciate issues relating to the study of the securities markets.
Programme Year Three
In addition to Core modules, choose two modules from the indicative list below.
Year Three Compulsory Modules
Applied Probability (MATH362)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of probabilistic model building for ‘‘dynamic" events occuring over time. To familiarise students with an important area of probability modelling.
Learning Outcomes 1. Knowledge and Understanding
After the module, students should have a basic understanding of:
(a) some basic models in discrete and continuous time Markov chains such as random walk and Poisson processes
(b) important subjects like transition matrix, equilibrium distribution, limiting behaviour etc. of Markov chain
(c) special properties of the simple finite state discrete time Markov chain and Poisson processes, and perform calculations using these.
2. Intellectual Abilities
After the module, students should be able to:
(a) formulate appropriate situations as probability models: random processes
(b) demonstrate knowledge of standard models
(c) demonstrate understanding of the theory underpinning simple dynamical systems
3. General Transferable Skills
(a) numeracy through manipulation and interpretation of datasets
(b) communication through presentation of written work and preparation of diagrams
(c) problem solving through tasks set in tutorials
(d) time management in the completion of practicals and the submission of assessed work
(e) choosing, applying and interpreting results of probability techniques for a range of different problems.
Mathematical Risk Theory (MATH366)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims to provide an understanding of the mathematical risk theory used in the study process of actuarial interest,
to provide an introduction to mathematical methods for managing the risk in insurance and finance (calculation of risk measures/quantities),
to develop skills of calculating the ruin probability and the total claim amount distribution in some non‐life actuarial risk models with applications to insurance industry,
to prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CT6 subject of the Institute of Actuaries (MATH366 covers 50% of CT6 in much more depth).
Learning Outcomes After completing the module students should be able to:
(a) Define the loss/risk function and explain intuitively the meaning of it, describe and determine optimal strategies of game theory, apply the decision criteria''s, be able to decide a model due to certain model selection criterion, describe and perform calculations with Minimax and Bayes rules.
(b) Understand the concept (and the mathematical assumptions) of the sums of independent random variables, derive the distribution function and the moment generating function of finite sums of independent random variables,
(c) Define and explain the compound Poisson risk model, the compound binomial risk model, the compound geometric risk model and be able to derive the distribution function, the probability function, the mean, the variance, the moment generating function and the probability generating function for exponential/mixture of exponential severities and gamma (Erlang) severities, be able to calculate the distribution of sums of independent compound Poisson random variables.
(d) Understand the use of convolutions and compute the distribution function and the probability function of the compound risk model for aggregate claims using convolutions and recursion relationships ,
(e) Define the stop‐loss reinsurance and calculate the (mean) stop‐loss premium for exponential and mixtures of exponential severities, be able to compare the original premium and the stoploss premium in numerical examples,
(f) Understand and be able to use Panjer''s equation when the number of claims belongs to the
R(a, b, 0) class of distributions, use the Panjer''s recursion in order to derive/evaluate the probability function for the total aggregate claims,(g) Explain intuitively the individual risk model, be able to calculate the expected losses (as well as the variance) of group life/non‐life insurance policies when the benefits of the each person of the group are assumed to have deterministic variables,
(h) Derive a compound Poisson approximations for a group of insurance policies (individual risk model as approximation),
(i) Understand/describe the classical surplus process ruin model and calculate probabilities of the number of the risks appearing in a specific time period, under the assumption of the Poisson process,
(j) Derive the moment generating function of the classical compound Poisson surplus process, calculate and explain the importance of the adjustment coefficient, also be able to make use of Lundberg''s inequality for exponential and mixtures of exponential claim severities,
(k) Derive the analytic solutions for the probability of ruin, psi(u), by solving the corresponding integro‐differential equation for exponential and mixtures of exponential claim amount severities,
(l) Define the discrete time surplus process and be able to calculate the infinite ruin probability, psi(u,t) in numerical examples (using convolutions),
(m) Derive Lundberg''s equation and explain the importance of the adjustment coefficient under the consideration of reinsurance schemes,
(n) Understand the concept of delayed claims and the need for reserving, present claim data as a triangle (most commonly used method), be able to fill in the lower triangle by comparing present data with past (experience) data,
(o) Explain the difference and adjust the chain ladder method, when inflation is considered,
(p) Describe the average cost per claim method and project ultimate claims, calculate the required reserve (by using the claims of the data table),
(q) Use loss ratios to estimate the eventual loss and hence outstanding claims,
(r) Describe the Bornjuetter‐Ferguson method (be able to understand the combination of the estimated loss ratios with a projection method), use the aforementioned method to calculate the revised ultimate losses (by making use of the credibility factor).
Life Insurance Mathematics II (MATH373)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims Provide a solid grounding in the subject of life contingencies for multiplelife, and in the subject of the analysis of life assurance, life annuities, pension contracts, multistate models and profit testing.
Provide an introduction to mathematical methods for managing the risk in life insurance.
Analyze problems of pricing and reserving in relation to contracts involving several lives.
Prepare the students to sit for the exams of CT5 subject of the Institute of Actuaries.
Be familiar with R programming language to solve life insurance problems.
Learning Outcomes Be able to explain, define and analyze the joint survival functions.
Understand the concept (and the mathematical assumptions) of the joint future life time random variables in continuous and discrete time and monthly. Be able to derive the distributions and the moment/variance of the joint future lifetimes.
Be able to define the survivals probabilities/death probabilities of either or both two lives, explain these types of probabilities and the force of interest intuitively, be able to calculate the different types of the survival/death probabilities in theoretical and numerical examples. Understand, define and derive the expected present values of different types of the life assurances and life annuities for joint lives, be able to calculate the expected present values of the joint life assurances and life annuities in theoretical and numerical examples.
Be familiar with R solfware and uses in actuarial mathematics
Statistical Methods in Actuarial Science (MATH374)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims Provide a solid grounding in analysis of general insurance data, Bayesian credibility theory and the loss distribution concept.
Provide an introduction to statistical methods for managing risk in nonlife insurance and finance.
Prepare the students adequately to sit for the exams of CT6 subject of the Institute of Actuaries.
Learning Outcomes Be able to apply the estimation methods described in (b) of the Syllabus for thedistribution described in (a) of the Syllabus, be able to make hypothesis testingdescribed in (b) of the Syllabus for the distribution described in (a) of the Syllabus.
Be able to estimate the parameters of the loss distributions when data complete/incomplete
using the method of moments and the method of maximum likelihood, be able to calculate the loss elimination ratio.Understand and use the Buhlmann model, the BuhlmannStraub model, be able to state the assumptions of the GLM models – normal linear model, understand the properties of the exponential family.
Be able to express the values of the life assurances in (d) of the Syllabus and the life annuities in (f) of the Syllabus in terms of the life table functions. Be able to use approximations for the evaluation of the life assurances in (d) of the Syllabus and the life annuities in (f) of the Syllabus based on a life table.
Be able to describe the properties of a time series using basic analytical and graphical tools.
Understand the definitions, properties and applications of well know time series
models, fit time series models to practical data sets and select the suitable models, be able to perform simple statistical inference (forecasting) based on the fitted models, estimate and remove possible trend and seasonality in a time series, analyse the residuals of a time series using stationary models.Stochastic Modelling in Insurance and Finance (MATH375)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims Be able to understand the stochastic modelling for different actuarial and financial problem.
Develop the necessary skills to construct asset liabilities models and to value financial derivatives.
Prepare the students to sit for the exams of CT8 subject of the Institute of Actuaries.
Learning Outcomes Understand the continuous time lognormal model of security prices, autoregressive model of security prices and other economic variables (e.g. Wilkie model). Compare them with alternative models by discussing advantages and disadvantages. Understand the concepts of standard Brownian motion, Ito integral, meanreverting process and their basic properties. Derive solutions of stochastic differential equations for geometric Brownian motion and OrnsteinUhlenbeck processes.
Acquire the ability to compare the realworld measure versus riskneutral measure. Derive, in concrete examples, the riskneutral measure for binomial lattices (used in valuing options). Understand the concepts of riskneutral pricing and equivalent martingale measure. Price and hedge simple derivative contracts using the martingale approach.
Be aware of the first and second partial derivative (Greeks) of an option price. Price zerocoupon bonds and interest–rate derivatives for a general onefactor diffusion model for the riskfree rate of interest via both riskneutral and stateprice deflator approach. Understand the limitations of the onefactor models.
Understand the Merton model and the concepts of credit event and recovery rate. Model credit risk via structural models, reduced from models or intensitybased models.
Understand the twostate model for the credit ratings with constant transition intensity and its generalizations: JarrowLandoTurnbull model.
Actuarial Models (MATH376)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 1
Be able to understand the differences between stochastic and deterministic modelling
2
Explain the need of stochastic processes to model the actuarial data
3
Be able to perform model selection depending on the outcome from a model.
4
Prepare the students adequately and to develop their skills in order to be ready to sit for the exams of CT4 subject of the Institute of Actuaries.
Learning Outcomes 1
Understand Use Markov processes to describe simple survival, sickness and marriage models, and describe other simple applications, Derive an appropriate Markov multistate model for a system with multiple transfers, derive the likelihood function in a Markov multistate model with data and use the likelihood function to estimate the parameters (with standard errors).
2
The KaplanMeier (or product limit) estimate, the NelsonAalen estimate , Describe the Cox model for proportional hazards Apply the chisquare test, the standardised deviations test, the cumulative deviation test, the sign test, the grouping of signs test, the serial correlation test to testing the adherence of graduation data,
3
Understand the connection between estimation of transition intensities and exposed to risk (central and initial exposed to risk) , Apply exact calculation of the central exposed to risk,
Year Three Optional Modules
Industrial Organisation (ECON333)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 50:50 Aims To apply the tools of microeconomics to the analysis of firms, markets and industries in order to understand the nature and consequences of the process of competition. These tools will also be applied to the evaluation of relevant government policy. This will extend knowledge and skills of microeconomic analysis by covering recent advances in theory as well as empirical analysis of relevant microeconomic topics.
Learning Outcomes Students will be able to use economic principles, concepts and techniques to discuss and analyse government policy and economic performance with reference to standard frameworks in Industrial Organisation. Students will be able to apply standard frameworks, including verbal, graphical, mathematical and statistical representations of economic concepts and models, to explain and evaluate the effects of a range of competitive behaviours by firms and how they are influenced by economic incentives.
Students will be able to analyse current issues and problems in business and industry.
Students will be able to compare, contrast and critically evaluate alternative schools of thought in Industrial Organisation with reference to empirical evidence.
Students will be able to conduct competent applied economic research by locating, selecting and analysing information relevant to the study of Industrial Organisation.
Students will be able to communicate effectively in writing and in accordance with a report specification
International Trade (ECON335)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 60:40 Aims To develop an appreciation and understanding of basic principles determining the observed patterns of trade in the increasingly globalised world economy.
Learning Outcomes After successful completion of this module, students will be able to:
recognise both the strengths and limitations of the basic Ricardian approach
understand the determinants of the terms of trade, in both theory and practice
recognise the implications of the observed behaviour of the terms of trade for both developed and less developed economies
appreciate the relationships between globalisation, economic performance
critically evaluate the roles, achievements and failures of various international institutions in the context of international economic performance
Competition and Regulation (ECON337)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 60:40 Aims To apply the tools of microeconomics to the analysis of firms, markets, consumers and regulators in order to understand the nature and consequences of the process of competition and regulation. These tools will also be applied to the evaluation of competition and government policy. This will extend knowledge and skills of microeconomic analysis by covering recent advances in theory as well as empirical analysis of relevant microeconomic topics.
Learning Outcomes Use economic principles, concepts and techniques to discuss and analyse:  the power and limitations of competition as a force for market regulation;
 government policy to regulate market power to protect firms, consumers and employees.
Apply standard frameworks, including verbal, graphical, mathematical and statistical representations of economic concepts and models, to explain and evaluate the effects of a range of behaviours by firms and regulators and how they are influenced by economic incentives.
Identify and analyse current issues and problems in regulation and propose solutions.
Compare, contrast and critically evaluate regulation of different industries and market failures.
Communicate effectively orally and in writing and in accordance with project specifications
Conduct independent research in applied economics
Deliver a professional quality formal presentation by exhibiting: clarity and appropriate pace; logical structure; credibility; effective use of visual aids/technology
Identify problems
Analyse problems
Offer viable solutions
Use economic principles, concepts and techniques to discuss and analyse government policy and economic performance.
Behavioural Finance (ACFI311)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims  Provide students with knowledge and understanding of theoretical and empirical limitations of and challenges to the efficient markets hypothesis

Present the psychological foundations of Behavioural Finance and how they impact upon investors’ rationality and arbitrage
Provide the opportunity for students to critically evaluate behaviourally induced market puzzles
Present key behavioural trading patterns from a theoretical perspective and outline their empirical design
Learning Outcomes Possess a good command of the key theoretical and empirical literature in behavioural finance
Have practiced skills of problemsolving and critical thinking
Be familiar with the main implications (theoretical and empirical) of Behavioural Finance findings
Construct and present critical evaluations of key academic papers in Behavioural Finance
Development of key skills in terms of writtencommunication (e.g. by completing formative class questions and assignment;through a summative assignment and examination)
Developmentof key skills in oral presentation (e.g. through group work)
Development of key skills in terms of classparticipation
Development of key skills in terms of planning &timemanagement (e.g. preparing for classes; observing assignment deadlines),problemsolving, critical thinking & analysis, numeracy (e.g. by applyingtheir extant quantitative knowledge in understanding behavioural financeissues) and initiative (e.g. searching relevant literature and information inpreparation of seminars and summative assignment)
 Provide students with knowledge and understanding of theoretical and empirical limitations of and challenges to the efficient markets hypothesis
Further Methods of Applied Mathematics (MATH323)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To give an insight into some specific methods for solving important types of ordinary differential equations.
To provide a basic understanding of the Calculus of Variations and to illustrate the techniques using simple examples in a variety of areas in mathematics and physics.
To build on the students'' existing knowledge of partial differential equations of first and second order.
Learning Outcomes After completing the module students should be able to:
 use the method of "Variation of Arbitrary Parameters" to find the solutions of some inhomogeneous ordinary differential equations.
 solve simple integral extremal problems including cases with constraints;
 classify a system of simultaneous 1storder linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases;
 classify 2ndorder linear partial differential equations and, in appropriate cases, find general or specific solutions. [This might involve a practical understanding of a variety of mathematics tools; e.g. conformal mapping and Fourier transforms.]
Mathematical Economics (MATH331)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims · To explore, from a gametheoretic point of view, models which have been used to understand phenomena in which conflict and cooperation occur.
· To see the relevance of the theory not only to parlour games but also to situations involving human relationships, economic bargaining (between trade union and employer, etc), threats, formation of coalitions, war, etc..
· To treat fully a number of specific games including the famous examples of "The Prisoners'' Dilemma" and "The Battle of the Sexes".
· To treat in detail twoperson zerosum and nonzerosum games.
· To give a brief review of nperson games.
· In microeconomics, to look at exchanges in the absence of money, i.e. bartering, in which two individuals or two groups are involved. To see how the Prisoner''s Dilemma arises in the context of public goods.
Learning Outcomes After completing the module students should:
· Have further extended their appreciation of the role of mathematics in modelling in Economics and the Social Sciences.
· Be able to formulate, in gametheoretic terms, situations of conflict and cooperation.
· Be able to solve mathematically a variety of standard problems in the theory of games.
· To understand the relevance of such solutions in real situations.
Applied Stochastic Models (MATH360)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims To give examples of empirical phenomena for which stochastic processes provide suitable mathematical models. To provide an introduction to the methods of stochastic model building for ''dynamic'' events occurring over time or space. To enable further study of the theory of stochastic processes by using this course as a base.
Learning Outcomes After completing the module students should have a grounding in the theory of continuoustime Markov chains and diffusion processes. They should be able to solve corresponding problems arising in epidemiology, mathematical biology, financial mathematics, etc.
Networks in Theory and Practice (MATH367)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 Aims To develop an appreciation of network models for real world problems.
To describe optimisation methods to solve them.
To study a range of classical problems and techniques related to network models.
Learning Outcomes After completing the module students should
. be able to model problems in terms of networks.
· be able to apply effectively a range of exact and heuristic optimisation techniques.
The programme detail and modules listed are illustrative only and subject to change.
Teaching and Learning
Your learning activities will consist of lectures, tutorials, practical classes, problem classes, private study and supervised project work. In Year One, lectures are supplemented by a thorough system of group tutorials and computing work is carried out in supervised practical classes. Key study skills, presentation skills and group work start in firstyear tutorials and are developed later in the programme. The emphasis in most modules is on the development of problem solving skills, which are regarded very highly by employers. Project supervision is on a onetoone basis, apart from group projects in Year Two.
Assessment
Most modules are assessed by a two and a half hour examination in January or May, but many have an element of coursework assessment. This might be through homework, class tests, miniproject work or key skills exercises.