Mathematics with Finance BSc (Hons) Add to your prospectus

  • Offers study abroad opportunities Offers study abroad opportunities
  • Opportunity to study for a year in China Offers a Year in China
  • This degree is accreditedAccredited

Key information


  • Course length: 3 years
  • UCAS code: G1N3
  • Year of entry: 2018
  • Typical offer: A-level : AAB / IB : 35 / BTEC : Applications considered
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Module details

Programme Year One

The Mathematics with Finance 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 Reporting and Finance

Subject CT3 - Probability & Mathematical Statistics: Statistical Theory I & II

Subject CT4 - Models: Applied Probability & Actuarial Models

You will take the following modules in Year 1:

ACFI101         Introduction to Financial Accounting

MATH 111      Mathematical IT Skills

MATH 101      Calculus 1

MATH 103      Introduction to Linear Algebra

ACFI 103        Introduction to Finance

MATH 122      Newtonian Mechanics

MATH 102      Calculus II

MATH            162      Introduction to Statistics

Year One Compulsory Modules

  • Calculus I (MATH101)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting80:20
    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)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    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 Co-ordinates

  • Introduction to Linear Algebra (MATH103)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting80:20
    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

  • Mathematical It Skills (MATH111)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting0:100
    Aims
  • To acquire key mathematics-specific 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.

  • Newtonian Mechanics (MATH122)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    Aims

    To provide a basic understanding of the principles of Classical Mechanics and their application to simple dynamical systems. 

    Learning Outcomes:

    After completing the module students should be able to analyse real world problems
    involving:

     - the motions of bodies under simple force systems

     - conservation laws for momentum and energy

     - rigid body dynamics using centre of mass,
       angular momentum and moments of inertia

    Learning Outcomes


    After completing the module students should be able to analyse
     real-world problems involving:

    ​the motions of bodies under simple force systems

    ​conservation laws for momentum and energy

    ​rigid body dynamics using centre of mass, angular momentum and moments

    ​oscillation, vibration, resonance

  • Introduction to Statistics (MATH162)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    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 goodness-of-fit tests

    ​to use the package Minitab to present data, and to make statistical analysis

  • Introduction to Financial Accounting (ACFI101)
    Level1
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting70:30
    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

  • Introduction to Finance (ACFI103)
    Level1
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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 risk-return 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.ACFI213        Corporate Financial Management

ACFI290         Financial Reporting & Finance

MATH201      Ordinary Differential Equations

MATH267      Financial Mathematics I

MATH262      Financial Mathematics II

MATH263      Statistical Theory And Methods I

MATH264      Statistical Theory And Methods II

 

Choose one module from

MATH227      Mathematical Models: Microeconomics and Population Dynamics

MATH241      Metric Spaces and Calculus

MATH261      Introduction To Methods Of Operational Research

MATH268      Operational Research: Probabilistic Models

ECON241       Securities Markets

MATH224      Introduction To The Methods Of Applied Mathematics

MATH266      Numerical Methods

Year Two Compulsory Modules

  • Corporate Financial Management for Non-specialist Students (ACFI213)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    The aim of the module is to provide an introduction to financial markets and to contextualise the application of mathematical techniques.

    Learning Outcomes

    ​Students will be equipped with the tools and techniques of financial management 

    ​Students will be able to interpret and critically examine financial management issues and controversies.

    ​Students will attain the necessary knowledge to underpin the more advanced material on  Quantitative Business Finance.

  • Financial Reporting and Finance (non-specialist) (ACFI290)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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 non-financial 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 OutcomesDescribe 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.

  • Ordinary Differential Equations (MATH201)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting90:10
    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 non-homogeneous) with constant coefficients matrix;

    - aware of a range of applications of ODE.

  • Financial Mathematics II (MATH262)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting90:10
    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)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting85:15
    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)
    Level2
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting90:10
    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.

Programme Year Three

  • Compulsory Modules:

    ACFI314         Quantitative Business Finance

    MATH362      Applied Probability

    MATH371      Numerical Analysis for Financial Mathematics

    MATH372      Time Series and its Applications in Economics

     

    Optional modules

    ECON212       Basic Economics I

    MATH323      Further Methods Of Applied Mathematics

    MATH363      Linear Statistical Models

    MATH367      Networks In Theory And Practice

    MATH365      Measure Theory and Probability

    ACFI310         Derivative Securities

    ACFI341         Finance & Markets

    MATH331      Mathematical Economics

    MATH360      Applied Stochastic Models

    MATH361      Theory Of Statistical Inference

    MATH366      Mathematical Risk Theory

    MATH376      Actuarial Models

Year Three Compulsory Modules

  • Quantitative Business Finance (ACFI314)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    ​This module aims to provide students with afundamental understanding of the core theoretical and empirical aspectsinvolved in corporate finance. In particular, the aims are that students will:

    1. Understand aspects of theoriesin corporate finance.
    2. Become familiar with a rangeof mathematical techniques commonly employed in corporate finance withparticular emphasis on bond valuation, stock valuation, firm valuation andassessing the probability that the firm will default on its debt obligations.
    3. Be aware that all mathematical models, which are dependenton a set of underlying assumptions, have limitations in the sense that the answerto a particular problem might change once the underlying assumptions change.

    Learning Outcomes

    ​Understand the principles of bonds and stocks valuation

    ​Understand how credit rating agencies assign credit rating scores to bonds

    ​Develop an understanding of issues involved in capital budgeting under uncertainty, market efficiency

    ​Understand portfolio theory, asset pricing models (CAPM, APT) and portfolio management

    ​An ability to analyse financial data in order to derive the optimal capital structure of firms

    ​Understand how option pricing theory can be used to firm valuation and assess the probability that a firm will default on its debt obligations

    ​An ability to analyse data in order to calculate Value at Risk as a single number summarising the total risk in a portfolio of financial assets.

    ​Understand the principles and practices involved in leasing, mergers and acquisitions

  • Applied Probability (MATH362)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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.

  • Numerical Analysis for Financial Mathematics (MATH371)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting80:20
    Aims

    1.

    To provide basic background in solving mathematical problems numerically, including understanding of stability and convergence of approximations to exact solution.

    2.

    To acquaint students with two standard methods of derivative pricing: recombining trees and Monte Carlo algorithms.

    3.

    To familiarize students with implementation of numerical methods in a high level programming language.

    Learning Outcomes

     

    Awareness of the major issues when solving mathematical problems numerically.

     

     

     

     

     

     

    Ability to analyse a simple numerical method for convergence and stability

    Ability to formulate approximations to derivative pricing problems numerically.

    ​Ability to program matlab for pricing options

  • Time Series and Its Applications in Economics (MATH372)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims

    1.

    Give students an understanding of econometric time-series methodology.

    2.

    Give students an understanding of important extensions include volatility models of financial time-series and multivariate (multiple equations) models such as vector error correction and related co-integrating error correction models.

    3.

    Present interesting applications that econometric time-series methodology can be applied.

    Learning Outcomes

     

    To be able to specify and demonstrate the distributional characteristics of a range of time series models

     

     

     

     

     

     

    To be able to estimate appropriate models of financial and economic time series for the purposes of forecasting and inference

    To be able to apply univariate and multivariate model selection and evaluation methods

    To be able to accommodate conditional heteroskedasticity, unit roots and cointegration in economic and financial time series analysis

Year Three Optional Modules

  • Basic Econometrics 1 (ECON212)
    Level2
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting70:30
    Aims
  • Econometrics is concerned with the testing of economic theory using real world data. This module introduces the subject by focusing on the principles of Ordinary Least Squares regression analysis. The module will provide practical experience via regular laboratory session.

     

  • ​This module also aims to equip students with the necessary foundations in econometrics to successfully study more advanced modules such as ECON213 Basic Econometrics II, ECON311  Methods of Economic Investigation: Time Series Econometrics and ECON312 Methods of Economic Investigation 2: Microeconometrics.

  • Learning OutcomesReinforce the  understanding of fundamental principles of statistics, probability and mathematics to be used in the context of econometric analysis

      ​Estimate simple regression models with pen and paper using formulae and with the econometric software EViews7

      ​Understand the assumptions underpinning valid estimation and inference in regression models

      ​Formulate and conduct intervals of confidence and tests of hypotheses

      ​Evaluate the impact that changes in the unit of accounts of variables and changes in the functional form of equations may have upon the results of OLS and their interpretation

      ​Assess the goodness of results by means of appropriate tests and indicators

      ​Assess predictions

      ​Extend analysis to the context of multiple linear regression

      ​Use EViews7 to estimate simple linear regression models  and multiple linear regression models

  • Further Methods of Applied Mathematics (MATH323)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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 1st-order linear partial differential equations, and to find the Riemann invariants and general or specific solutions in appropriate cases;

    -     classify 2nd-order 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.]

  • Linear Statistical Models (MATH363)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    Aims

    ·      to understand how regression methods for continuous data extend to include multiple continuous and categorical predictors, and categorical response variables.

    ·      to provide an understanding of how this class of models forms the basis for the analysis of experimental and also observational studies.

    ·      to understand generalized linear models.

    ·      to develop familiarity with the computer package SPSS.

    Learning Outcomes

    After completing the module students should be able to:

            understand the rationale and assumptions of linear regression and analysis of variance.

    ·      understand the rationale and assumptions of generalized linear models.

    ·      recognise the correct analysis for a given experiment.

    ·      carry out and interpret linear regressions and analyses of variance, and derive appropriate theoretical results.

    ·      carry out and interpret analyses involving generalised linear models and derive appropriate theoretical results.

    ·      perform linear regression, analysis of variance and generalised linear model analysis using the SPSS computer package.

  • Networks in Theory and Practice (MATH367)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting100:0
    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.

  • Measure Theory and Probability (MATH365)
    Level3
    Credit level15
    SemesterFirst Semester
    Exam:Coursework weighting90:10
    Aims

    The main aim is to provide a sufficiently deepintroduction to measure theory and to the Lebesgue theory of integration. Inparticular, this module aims to provide a solid background for the modernprobability theory, which is essential for Financial Mathematics.

    Learning Outcomes

    ​After completing the module students should be ableto:

    ​master the basic results about measures and measurable functions;

    master the basic results about Lebesgue integrals and their properties;

    ​​​​to understand deeply the rigorous foundations ofprobability theory;

    ​to know certain applications of measure theoryto probability, random processes, and financial mathematics.

  • Derivative Securities (ACFI310)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims

    This courseprovides an introduction to derivative securities.  Alternative derivative securities likeForwards, Futures, Options, and Exotic Derivative Contracts will bediscussed.  This incorporates detailingthe properties of these securities. Furthermore, a key aim is to outline how these assets are valued.  Also the course demonstrates the use ofderivatives in arbitrage, hedging and speculation. Finally, practicalapplications of derivatives and potential pitfalls are discussed.

     

    The class is runas a discussion based forum and students are expected to read all necessarymaterials prior to each session.

     

    Learning Outcomes

     Describe the principles of option pricing.

    Compare and contrast alternative fair valuation techniques for pricing derivative instruments.

    ​Explain the biases in option pricing models.

    ​Apply an appropriate pricing model to a variety of contingent claim securities.

    Recognize the trading strategy appropriate to expected future market conditions.

    Derive and apply evolving models of derivative options to effectively manage risk transfer and assess their behaviour in the face of volatile financial and economic conditions.

  • Finance and Markets (ACFI341)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims

    The module builds onthe foundations of the existing finance modules and aims to give students asolid grounding in terms of understanding the recent global financial crisisand a wide range of risk management tools available to financial managers.Particular emphasis is placed on the issue of risk measurement. The followingtypes of risk will be analysed extensively

     

    (i)             interestrate risk

    (ii)           marketrisk

    (iii)          creditrisk

    (iv)          liquidityrisk

    (v)           capitaladequacy and

    (vi)          sovereignrisk

     

    The class is run as a discussion based forum and you are expected toread all necessary materials prior to each session

    Learning OutcomesStudents will be able to understand how risk management contributes to value creation

    ​Students will be able to understand how the global market for credit operates

    ​Students will be able to explain the causes of the recent global credit crisis

    ​Students will be able to develop an overview the risks facing a modern corporation

    ​Students will be able to analyse the effects of interest rate volatility on risk exposure

    ​Students will be able to examine market risk, which results when companies actively trade bonds, equities and other securities

    ​Students will be able to examine how credit risk adversely impacts a financial institution’s profits

    ​Students will be able to analyse the problems created by liquidity risk

    ​Students will be able to become familiar with the concept of capital adequacy and also with the Basel Accords

    Students will be able to examine several aspects of sovereign lending and the underlying risks

  • Mathematical Economics (MATH331)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    Aims

    ·      To explore, from a game-theoretic 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 two-person zero-sum and non-zero-sum games.

    ·      To give a brief review of n-person 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 game-theoretic 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)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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 continuous-time Markov chains and diffusion processes. They should be able to solve corresponding problems arising in epidemiology, mathematical biology, financial mathematics, etc.

  • Theory of Statistical Inference (MATH361)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting90:10
    Aims

    To introduce some of the concepts and principles which provide theoretical underpinning for the various statistical methods, and, thus, to consolidate the theory behind the other second year and third year statistics options.

    Learning Outcomes

    After completing the module students should have a good understanding of the classical approach to, and especially the likelihood methods for, statistical inference. 

    The students should also gain an appreciation of the blossoming area of Bayesian approach to inference

  • Mathematical Risk Theory (MATH366)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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).

  • Actuarial Models (MATH376)
    Level3
    Credit level15
    SemesterSecond Semester
    Exam:Coursework weighting100:0
    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 multi-state model for a system with multiple transfers, derive the likelihood function in a Markov multi-state model with data and use the likelihood function to estimate the parameters (with standard errors).

    2

    The Kaplan-Meier (or product limit) estimate, the Nelson-Aalen estimate , Describe the Cox model for proportional hazards Apply the chi-square 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,

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 first-year 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 one-to-one 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, mini-project work or key skills exercises.