# Actuarial Mathematics and Risk Modelling

## Course summary

Course code: MATH0160
Level: 6
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences

## Specification

### Pre and co requisites

Probability and Statistical Analysis, Advanced Calculus and Mathematical Methods, or equivalent

### Aims

An Actuary is charged with assessing the uncertainties involved in providing insurance. The quantification of these uncertainties requires statistical methods with some mathematical development. This course investigates modern actuarial modelling and examines the basic techniques used in actuarial analysis. The aim is to provide students with a firm mathematical and statistical background so that they can apply mathematical and statistical models to assess risk factors and apply stochastic models appropriate to the representation of the risk process. By doing so, the students can analyse and solve practical problems in actuarial sciences.

### Learning outcomes

On successful completion of this course a student will be able to:

1. recognize the basic concepts and standard terms in actuarial science.
2. apply the typical long-tailed distributions representing claim size and those representing claim number, use appropriate methods to extract relevant moment information, and derive consequential information about total claim size.
3. use life tables, determine and manipulate the financial functions relating to life insurance.
4. apply appropriate mathematical methods in actuarial calculations and obtain solutions for some problems in risk theory.
5. make effective use of statistical models to analyse the risk factors for categories of policy holders.
6. critically appraise the results of your analysis, and appreciate disciplines and forms of professional practice beyond Actuarial science, and draw connections between them.

### Indicative content

Moments and Moment Generating Functions, Standard long-tailed distributions, Poisson and Negative Binomial distributions. Safety loadings, Excesses, Reinsurance and initial reserves.
Life tables, Life time distribution and force of mortality models.
Discounted financial functions for life insurance, endowments and annuities.
Risk factors for claim frequency, Stochastic model and solution for the ruin problem.

### Teaching and learning activity

Concepts, methods and basic conclusions will be introduced and explained in lectures.
Problem solving and technique training will be done through tutorials.
Practical work using statistical software will be done through laboratory sessions.

### Assessment

Summative assessment:
Coursework - 50%
An individual take-home assignment on topics covered during the first 8 weeks of the term assessing specified learning outcomes 1, 2, 3 and 6.

Exam - 50%
A 3-hour long closed book examination assessing all learning outcomes 1 to 6 with the format of answer any “Four out of Six Questions”
A copy of English Life Table, Formulae sheet & Stats Tables to be provided

Formative assessment: weekly tutorial exercises