# BSc Actuarial Science and Mathematics / Course details

Year of entry: 2024

## Course unit details:Risk Theory

Unit code MATH39542 10 Level 3 Semester 2 Department of Mathematics No

### Overview

Following up on the course unit Actuarial Insurance this unit introduces further concepts and models relevant to the non-life industry, in particular the important concept of ruin in a risk model is discussed.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Probability 2 MATH20701 Pre-Requisite Compulsory
Actuarial Insurance MATH20972 Pre-Requisite Compulsory
Actuarial Science only

### Aims

This unit aims at providing students with a further grounding in the important statistical and probabilistic techniques and models relevant to the non-life insurance industry.

### Learning outcomes

On completion of this unit, successful students will be able to:
1. compare and contrast the Bayesian approach and the frequentist approach to Statistics.
2. discuss the Bayesian approach to decision theory and inference problems, and determine the Bayesian solution for such problems.
3. discuss the assumptions and goals of credibility theory, and compute the types of credibility estimates seen in the course.
4. discuss the main categories making up the field of machine learning and categorise given situations accordingly.
5. execute and evaluate principal component analysis and clustering on appropriate data sets.
6. discuss and evaluate dependence between random variables using copulas and related concepts.

### Syllabus

(i) Bayesian Statistics: decision theory and inference
(ii) Credibility theory: Bayes, Buhlmann and Buhlmann-Straub
(iii) Machine Learning: overview of the field & main categories, Principal Components Analysis & Clustering
(iv) Copulas: examples & properties, generators, Kendall's tau and correlation

### Assessment methods

Method Weight
Other 20%
Written exam 80%
• Coursework 20% (one piece of take home coursework).
• Examination at the end of the semester, 80%.

### Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

Insurance Risk and Ruin. Dickinson, D.C.M. (ISBN: 9780521176750)

### Study hours

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

### Teaching staff

Staff member Role
Kees Van Schaik Unit coordinator