ST33815 Actuarial Models
Introductory description
This module runs in Term 2 and is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.
Prerequisites:
Statistics Students: ST218 Mathematical Statistics A AND ST219 Mathematical Statistics B
NonStatistics Students: ST220 Introduction to Mathematical Statistics
Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries (IFoA) modules CS2 and CM1. (Independent application with the IFoA may be required to receive the exemption.)
Module aims
To cover part of the syllabus for Institute of Actuaries exam CS2 and CM1.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Principles of actuarial modelling
 Principles of stochastic processes
 Markov chains and Markov processes
 Survival models: lifetimes, curtate future lifetime, expected value and variance.
 Estimation procedures for lifetime distributions: Kaplanâ€”Meier estimate, Cox model
 Multistate Markov models.
 Maximum likelihood estimators for transition intensities in multistate models.
 Binomial model of mortality.
 Estimating mortality rates by age: exact methods, census approximations
 Process of graduation.
 Statistical tests for life tables.
Learning outcomes
By the end of the module, students should be able to:
 Describe the principles of actuarial modelling
 Describe the general principles of stochastic processes and their classification into different types.
 Define and apply a Markov chain.
 Define and apply a Markov process.
 Explain the concept of survival models.
 Describe estimation procedures for lifetime distributions
 Derive maximum likelihood estimators for the transition intensities in models of transfers between states with piecewise constant transition intensities.
 Describe the Binomial model of mortality, derive a maximum likelihood estimator for the probability of death and compare the Binomial model with the multiple state models.
 Describe how to estimate transition intensities depending on age, exactly or using the census approximation.
 Describe how to test crude estimates for consistency with a standard table or set of graduated estimates and describe the process of graduation.
Indicative reading list
View reading list on Talis Aspire
Subject specific skills
TBC
Transferable skills
TBC
Study time
Type  Required  Optional 

Lectures  28 sessions of 1 hour (16%)  2 sessions of 1 hour 
Seminars  8 sessions of 1 hour (4%)  
Tutorials  (0%)  
Private study  112 hours (63%)  
Assessment  30 hours (17%)  
Total  178 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading of actuarial syllabus, practice exercises and preparing for class tests and the examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D1
Weighting  Study time  

Computer Based Assessment 1  10%  15 hours 
Multiple choice quiz which will take place during the term that the module is delivered. 

Computer Based Assessment 2  10%  15 hours 
Multiple choice quiz which will take place during the term that the module is delivered. 

Online Examination  80%  
You will be required to answer all questions on this examination paper. ~Platforms  Moodle

Assessment group R
Weighting  Study time  

Online Examination  Resit  100%  
You will be required to answer all questions on this examination paper. ~Platforms  Moodle

Feedback on assessment
Solutions and cohort level feedback will be provided for the class tests within 4 weeks of the test. Your paper will not be returned as it must be retained for the external examiners but you may make an appointment with the module leader to view your script and receive individual feedback.
Solutions and cohort level feedback will be provided after the Summer examination.
Courses
This module is Optional for:
 Year 3 of UCSAG4G1 Undergraduate Discrete Mathematics
 Year 3 of UCSAG4G3 Undergraduate Discrete Mathematics
 Year 4 of UCSAG4G2 Undergraduate Discrete Mathematics with Intercalated Year

USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 3 of G300 Mathematics, Operational Research, Statistics and Economics
 Year 4 of G300 Mathematics, Operational Research, Statistics and Economics

USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)
 Year 4 of USTAG1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list A for:
 Year 3 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics

USTAG301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
 Year 3 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
 Year 4 of G30E Master of Maths, Op.Res, Stats & Economics (Actuarial and Financial Mathematics Stream) Int
This module is Option list B for:
 Year 3 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics