# BSc Actuarial Science and Mathematics

Year of entry: 2022

## Course unit details:Actuarial Insurance

Unit code MATH20972 10 Level 2 Semester 2 Department of Mathematics No

### Overview

This course unit provides a basic knowledge of some of the major notions and models of probability and statistics which are particularly relevant to non-life insurance. The course covers part of Subject CT6, one of the core technical modules from the educational program of the Actuarial Profession.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Financial Mathematics for Actuarial Science 1 MATH10951 Pre-Requisite Compulsory
MATH20972 pre-requisites

For students on the Actuarial Science and Mathematics programme only.

### Aims

The aim of this unit is to provide to students a further grounding in several stochastic and statistical techniques of particular relevance to the non-life insurance industry.

### Learning outcomes

On completion of this unit, successful students will be able to:

• Analyse games and solve decision-making problems using game and decision theory.
• Model situations of the type arising in the insurance industry using probabilistic tools.
• Evaluate aspects of probabilistic models relevant for financial risk, and discuss the consequences in terms of risk and decision-making.
• Select and use approximation methods in probabilistic models, and describe their limitations.
• Compute reserves in an insurance context.
• Generate, describe and analyse simulation algorithms for random variables.

### Syllabus

1.Decision Theory. Two person zero sum games, randomised strategies, saddle points, statistical games (with data), Bayes criterion, minimax criterion.

2.Loss Distributions. Properties of loss distributions, actuarial interpretation, effect of different types of reinsurance.

3.Run-off triangles. Several methods for computing required reserves in the context of run-off triangles.

4.Risk models. Aggregated claim amounts modeled by compound distributions in elementary and more advanced form, results about their moment generating functions/moments etc., several standard compound distributions, effect of different types of reinsurance.

5.Monte Carlo methods. The basics of the Monte Carlo simulation method: simulation using the cdf and acceptance-rejection, variance reduction techniques etc.

### Assessment methods

Method Weight
Other 20%
Written exam 80%

1.Coursework 20%

2.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.

### Recommended reading

• Core Reading: Subject CT6, Statistical Methods. Produced by the Actuarial Education Company (www.acted.co.uk).
• Loss models: from data to decisions (2008), third edition. Stuart A. Klugman, Harry H. Panjer and Gordon E. Willmot.
• Monte Carlo Methods in Financial Engineering (2004). Paul Glasserman.
• Non-life Insurance Mathematics. An Introduction with Stochastic Processes (2004),second edition. Thomas Mikosch.

### Study hours

Scheduled activity hours
Lectures 12
Tutorials 12
Independent study hours
Independent study 76

### Teaching staff

Staff member Role
Kees Van Schaik Unit coordinator

### Additional notes

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

·         You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently

·         You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week

·         There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises

·         In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.

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