Topic outline

  • General

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    The particular focus of this module is on mathematical models for Survival and Mortality which are widely used in Life Assurance, demographics and medical statistics. We will consider the mathematical foundations, a number of modelling approaches and a range of model applications. The syllabus is designed to meet the requirements of the CS2 examination of the Institute & Faculty of Actuaries, "Risk Modelling and Survival Analysis".

  • Week 1 : Introduction, Modelling Mortality

    Welcome to Survival Models. In this first week we will introduce the module and its place in both the study of actuarial science and a wide range of practical applications. We will look at the general shape of human survival probability distributions and consider heterogeneity in mortality. This will give us an excellent foundation for the module.

    There will be lectures on Monday (MB203) and Thursday (Eng2016) at 11.00am

  • Week 2 : Survival Model Concepts

    This week we will cover Survival Model Concepts - the key elements of actuarial mathematics that underpin the models we will examine later in the module. Much of the material from this week will build upon Actuarial Mathematics II (MTH5125) but we will also make sure that anyone who hasn't studied actuarial mathematics before is fully caught up. Once again there will be 4 hours of timetabled activities on Monday and Thursday at 11.00.

  • Week 3: Censoring and the Kaplan Meier Estimate

    Having developed general survival model concepts last week, we are now ready to move on to the first of our Survival Models - the Kaplan Meier estimate. This is an example of a 'non-parametric' estimate of survival which is used in medical trials amongst other applications. Once again lectures will be Monday and Thursday morning. We will also include a session on how to implement the model in R.

  • Assessed Coursework 1

    In this section you will find a PDF document with the coursework question and instructions [to be released after the week 3 lectures on Thursday 12th October], a CSV file with the dataset for the question and a submission point to upload your solution in a MS Word document by 5pm UK time on Wednesday 18th October (week 4). This assessment counts towards 15% of your module mark and is based on the material in week 3 using R programming.

  • Week 4: Proportional Hazard Models

    We now move from non-parametric to parametric models of survival and the use of likelihood estimates. First we will look at proportional hazard models which can be used to model mortality and survival in relation to a number of factors such as age, health, socio-economic conditions. 

  • Week 5: Markov Processes and Multi State Models

    We now move to a different framework for parametric modelling - the Markov Process, which will lead us into Multi-State models.  Material in this section will link to your studies in Random Processes. These Models can be used for quite complex scenarios such as the social security system of a country.

  • Week 6: Statistical approximations to Multi State Models

    We will complete the set of survival models this week moving on from Multi State models to look at approximations to these that are derived from assuming well known Statistical distributions - the Binomial and Poisson. We will then look at ways to compare the different models we have considered over the last four weeks in this module. 

  • Week 7: Reading Week no lectures

  • Week 8: Exposed to Risk

    Having looked at different survival models in weeks 3,4,5,6, we now move in the next 3 weeks to consider how these models are used in practice and are tested in a life assurance context in particular. We begin with Exposed to Risk.  In previous years, students have found exam questions on this topic to be the most troublesome ones - so I would recommend taking time to go through the material carefully this week.

  • Assessed Coursework 2

    In this section you will find a PDF document with the coursework question and instructions , 3 CSV files with the data needed for the question and a submission point to upload your solution in a MS Word document by 5pm UK time on Friday 24 November (week 9). This assessment counts towards 15% of your module mark.

  • Week 9: Statistical Tests

    We now come to how actuaries use survival model outputs for practical work in life assurance. The key task here is called 'Graduation' which takes force of mortality or rate of mortality from the models we considered in weeks 2-6 and uses them to construct the mortality tables like those used for Life Assurance premium and reserve calculations in Actuarial Maths II. We will spend two weeks on this area. In week 10 we will look at techniques for doing a Graduation but before that we consider some statistical tests of the model output. 

  • Week 10: Graduation Methods

    We continue with Graduation - moving from statistical tests of how well a graduated table or standard table fits observed mortality on to questions of how actuaries actually do the graduation. 

  • Week 11: Mortality Projections

    Our final topic in this module is Mortality Projections - models of how survival and mortality rates might change in future years. We will give an overview of different methods used. The implementation of these projections links to Time Series which many of you will study next semester.

  • Syllabus

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  • Module description

    The length of people’s lives is of crucial importance in the Insurance and Pensions industry so models for survival must be studied by trainee Actuaries. This module considers a number of approaches to modelling data for survival and mortality. These include parametric and non-parametric statistical approaches and methods developed by actuaries using age-specific death rates. We will also look at tests of the consistency of crude (not exact but useful) estimates with a standard table using a number of non-parametric methods.

  • Module aims and learning outcomes

  • assessment

  • teaching team

  • hints and tips

  • where to get help

  • module handbook

  • general course materials

  • coursework

  • exam papers

  • Week 12: Revision

    Having completed the course content, the last week will be given over to revision lectures and some past paper and exam-style questions.

  • Assessment information

    • Assessment Pattern 

      Assessment for this module is 70% by final exam in the January 2024 examination period and 30% by two assessed courseworks (see below). 

      Format and dates for the in-term assessments 

      There are two in-term assessments, each contributing 15% to the overall module mark. These both require calculations in R programming alongside some written analysis of the modelling results. The first assessed coursework is set in week 3 for submission in week 4 and the second one is set in week 8 for submission in week 9.

      Format of final assessment 

      The exam will be 3 hours, handwritten, on campus and the format of the paper will be similar to that in previous years for this module. Past papers and solutions can be found in the week 12 section of the module QM Plus page.

      Description of Feedback

       Feedback will be given on each assessed coursework by way of comments annotated to the MS Word coursework submission and accessed via QM Plus. As well as assessed coursework, exercise sheets are provided each week for further practice.

  • Reading List Online

  • Q-Review