Mathematics with Finance BSc (Hons)
 Course length: 3 years
 UCAS code: G1N3
 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 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 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 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)
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
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.
Newtonian Mechanics (MATH122)
Level 1 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 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 inertiaLearning Outcomes
After completing the module students should be able to analyse
realworld 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)
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
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
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.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 Nonspecialist Students (ACFI213)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 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 (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.
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.
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.
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)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 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:
 Understand aspects of theoriesin corporate finance.
 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.
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)
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.
Numerical Analysis for Financial Mathematics (MATH371)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 80:20 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)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 Aims 1.
Give students an understanding of econometric timeseries methodology.
2.
Give students an understanding of important extensions include volatility models of financial timeseries and multivariate (multiple equations) models such as vector error correction and related cointegrating error correction models.
3.
Present interesting applications that econometric timeseries 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)
Level 2 Credit level 15 Semester First Semester Exam:Coursework weighting 70:30 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 Outcomes Reinforce 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)
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.]
Linear Statistical Models (MATH363)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 100:0 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)
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.
Measure Theory and Probability (MATH365)
Level 3 Credit level 15 Semester First Semester Exam:Coursework weighting 90:10 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)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 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)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 100:0 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 Outcomes Students 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)
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.
Theory of Statistical Inference (MATH361)
Level 3 Credit level 15 Semester Second Semester Exam:Coursework weighting 90:10 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)
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).
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,
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.