# ST402-15 Risk Theory

22/23
Department
Statistics
Level
Larbi Alili
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### Introductory description

This module runs in Term 2 and is available for students on a course where it is a listed option. It is not available as an Unusual Option to students with their home department outside Statistics.

Prerequisites:
Integrated Masters: ST318 Probability Theory
MSc: ST903 Statistical Methods

Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries module CM2. (Independent application with the IFoA may be required to receive the exemption.)

##### Module aims

This module partly fulfils the aim of the MMORSE stream in Actuarial and Financial Mathematics to enable students to study more deeply the area named in the stream. It will cover material of use in general insurance such as loss distributions, ruin problems in compound Poisson processes and credibility theory.

##### 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.

Decision theory.
Loss distributions: standard examples. Excesses and retention limits.
Bayesian Statistics.
Ruin problem in compound Poisson processes; the adjustment coefficient and
Lundberg's inequality.
Credibility theory: Bayes and empirical Bayes approaches.
Run-off triangles: projection of future development; chain ladder method.
Use of GLMs in general insurance.
Time Series.
Simulation of a Stochastic Process.

##### Learning outcomes

By the end of the module, students should be able to:

• Know how probability models are used in general insurance
• Understand the concept of methods of re-insurance to hedge against risk.

P.J. Boland (2007) Statistical and probabilistic methods in actuarial sciences.
C.D. Daykin, T. Pentikainen, M. Pesonon (1994) Practical Risk Theory for Actuaries.
S.A. Klugman (1985) Loss distributions.
P. McCullagh, J.A. Nelder. (1989) Generalized Linear Models. Chapman and Hall, London.

TBC

TBC

## Study time

Type Required Optional
Lectures 30 sessions of 1 hour (20%) 2 sessions of 1 hour
Tutorials 9 sessions of 1 hour (6%)
Private study 111 hours (74%)
Total 150 hours
##### Private study description

Weekly revision of lecture notes and materials, wider reading, 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 D2
Weighting Study time
Class Test 1 10%

Term 2 Week 7

Class Test 2 10%

Term 2 Week 10

In-person Examination 80%

• Students may use a calculator
##### Assessment group R1
Weighting Study time
In-person Examination - Resit 100%

• Students may use a calculator
• Graph paper
• Cambridge Statistical Tables (blue)
##### Feedback on assessment

Feedback on Class Test 1 will be returned after 2 weeks, and feedback on Class Test 2 will be returned after 3 weeks, following each test. If the number of registered students is less than 30 then they will be given the opportunity to receive feedback via face-to-face meetings. Solutions and cohort level feedback will be provided for the examination.

## Courses

This module is Optional for:

• Year 1 of TMAA-G1PE Master of Advanced Study in Mathematical Sciences
• Year 1 of TSTA-G4P1 Postgraduate Taught Statistics
• USTA-G300 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

This module is Option list A for:

• Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated
• USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
• Year 3 of G1G3 Mathematics and Statistics (BSc MMathStat)
• Year 4 of G1G3 Mathematics and Statistics (BSc MMathStat)
• USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
• Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
• Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)

This module is Option list D for:

• Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

This module is Option list E for:

• Year 4 of USTA-G300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
• Year 5 of USTA-G301 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated

Assessments dates for Statistics modules, including coursework and examinations, can be found in the Statistics Assessment Handbook.