Bachelor of Science (BSc)

BSc Mathematics with Placement Year

Strengthen your employability by taking our Placement Year programme.
  • Duration: 4 years
  • Year of entry: 2025
  • UCAS course code: G101 / Institution code: M20
  • Key features:
  • Industrial experience
  • Accredited course

Full entry requirementsHow to apply

Fees and funding

Fees

Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £34,500 per annum. For general information please see the undergraduate finance pages.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Course unit details:
Mortality Modelling in Insurance

Course unit fact file
Unit code MATH39562
Credit rating 10
Unit level Level 3
Teaching period(s) Semester 2
Available as a free choice unit? No

Overview

How long do humans live? Or other living beings? How long does it take for some mechanical system to experience component failure? Or for the next economic crisis to happen? Or for a next major scientific breakthrough to shake up our lives? Or for it to stop raining in Manchester? These are the kind of questions that Survival Analysis is trying to answer: a branch of statistics that builds a fine grained model based on currently available data and predicts the expected waiting time until the next relevant event.

The first half of this course introduces and discusses Survival Analysis more in general, while the second half focuses on applications in life insurance and pensions as well as related techniques for mortality estimation and projection.

This course is fundamental for students on the BSc Actuarial Science & Maths, but is also very suited for other students with an interest in Statistics/Survival Analysis. The mathematical techniques are all rooted in Statistics and no prior knowledge of insurance related concepts is assumed. 

Pre/co-requisites

Unit title Unit code Requirement type Description
Probability and Statistics 2 MATH27720 Pre-Requisite Compulsory
Linear Regression Models MATH27711 Pre-Requisite Compulsory
MATH 39562 PRE REQS

Aims

The unit aims to: discuss the field of Survival Analysis and related statistical techniques prominently used in life insurance, pensions, economics, engineering and elsewhere

Learning outcomes

  • Derive whether a given censoring mechanism for the purpose of estimating survival times is independent or not.
  • Perform estimation of truncated and censored survival times using non-parametric, parametric and semi-parametric methods and analyse the results.
  • Perform a variety of hypothesis tests (in particular, 2-sample, likelihood related and graphical tests) associated with the estimation procedures and interpret the outcomes.
  • Explain and apply a variety of commonly used methods for mortality forecasting.
  • Use the census approximation in order to estimate mortality rates given census data.
  • Apply any of a number of commonly used statistical tests to derive whether a given graduation of mortality rates is successful. 

Syllabus

1. Survival analysis: non-parametric models (incl. Kaplan-Meier & Nelson-Aalen); parametric models; survival & (cumulative) hazard function; residual & expected lifetimes; using the R package ‘survival’

2. The Cox proportional hazards model

3. Estimation of mortality rates: Poisson model; graduation; goodness of fit tests

4. Mortality projection: the Lee-Carter model 
 

Teaching and learning methods

The course will be delivered via 22 lectures in which the course materials will be explained and discussed, supported by a set of detailed, typeset lecture notes. Further there will be 11 tutorial sessions, during which students work on exercises to cement the materials and they can get individual feedback on their understanding. Solutions to the exercises will also be provided.

Note: prior to the exam students will be able to get individual feedback on their solutions of past exam paper questions (and otherwise). 

Assessment methods

Method Weight
Written exam 70%
Written assignment (inc essay) 30%

Feedback methods

Generic feedback will be available after the exam period.

Coursework feedback is given as soon as marking is complete both individually as well as class level

Recommended reading

No further reading required, lecture notes (and the example sheets) are sufficient.

Suggestions for further reading:

Aalen, Odd O., Borgan, Ørnulf and Gjessing, Håkon K. Survival and event history analysis: A process point of view. Springer, New York 2008.

Kleinbaum, David G. and Klein, Mitchel. Survival analysis: A self-learning text. 3rd edition, Springer, New York 2012. 

Study hours

Scheduled activity hours
Lectures 22
Tutorials 11
Independent study hours
Independent study 67

Teaching staff

Staff member Role
Yuk Ka Chung Unit coordinator

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