Actuarial Mathematics BSc (Hons)

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 subject-by-subject 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

You will take the following modules in Year 1:

• Calculus I
• Introduction to Linear Algebra
• Calculus II
• Financial Accounting
• Principles of Microeconomics
• Introduction to Statistics
• Introductory Finance
• Principles of Macroeconomics

Tutorials for foundation modules are in groups of about 8 students.

Compulsory modules

• 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

  After completing the module students should be able to:

  ·      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

  After completing the module, students should be able to:

  ·         use Taylor series to obtain local approximations to functions;

  ·         obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables;

  ·         evaluate double integrals using Cartesian and polar co-ordinates.

• 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

  After completing the module students should be ableto:

  •     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

  After completing this module students should be able

  -         to describe statistical data;

  -         to use the Binomial, Poisson, Exponential and Normal distributions;

  -         to perform simple goodness-of-fit 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

  To acquaint students with elementary microeconomic theory. We will cover: basic definitions and concepts in (micro)economics, consumer theory, producer theory, perfect competition, imperfect competition, externalities and public goods.

  The mathematics content will include some basic algebra, equations of the straight line, elementary calculus.

  Learning Outcomes

  After this module students should have achieved a theoretical background in the elementary concepts of microeconomic theory   

  
  

  ​  Students should have learned how to apply these concepts.

• 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
  

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  ·         Explainthe behaviour of economic aggregates such as national income, inflation andunemployment over time

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  ·         Explainand assess government policy in a range of policy situations

  ·         Explainthe framework of national income accounting

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  ·         Usegraphical and algebraic modelling to analyse the economy and economic policy

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  ·         Explainthe interconnections between the markets for goods, money and labour

  ·         Explainthe principal influences on long-term growth and the short-run fluctuation inoutput around the long-run growth trend

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  ·         Locate,select and analyse information relevant to assessing the state of the economyand economic policy

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.

• Financial Mathematics I
• Financial Mathematics II
• Statistical Theory and Methods I
• Statistical Theory and Methods II
• Life Insurance Mathematics I
• Financial Reporting and Finance

Please note that along with the compulsory module, two modules in Life Insurance and Financial Reporting & Finance must be taken.

Compulsory modules

• 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 no-arbitrage.

  Learning Outcomes

  After completing the module students should be able to:

  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 m-thly, (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 non-level payments, immediate (or due) , payable m-thly, (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 index-linked 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 dollar-weighted 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.

• 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).