MMath Mathematics and Statistics

A “risk” is any future gain/loss of uncertain size, and obviously we would like to be able to “manage” such risks. From a mathematical perspective that entails: model and analyse the risk, in order to understand the situation and make sensible decisions. The uncertainty involved means that random variables and more generally probability theory are very important fundamentals. Building on these, many tools and techniques for risk management have been developed over time, and in this course we will discuss some of the most prominent ones. Although the focus will mainly be on examples from/applications in finance, insurance and related, the possible applications are much more diverse. This course also contains some light use of the software package R.

Note: this course does not consider (investing in) financial markets, there are several other courses dedicated to that topic. 

MATH37542 Pre-Requisites: MATH27720

The unit aims to: introduce students to a number of (mathematical/quantitative) risk management tools prominent in finance, insurance, project management and elsewhere. 

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

 

ILO1. recall and create suitable probabilistic models for modelling a real world risk context    

ILO2. construct algorithms for simulating samples from probability distributions and utilise those samples for risk management tasks

ILO3. describe and analyse probabilistic dependency structures using copulas

ILO4. recall, design and analyse risk sharing arrangements

ILO5. employ compound distributions to describe and evaluate risk aggregation

ILO6. define and assess basic credit risk models

ILO7. where appropriate, use basic functionality of the software package R to complement the theoretical elements of this course 

1. Monte Carlo simulations

2. Copulas

3. Premium principles & risk measures

4. Sharing and aggregating risks

5. Credit risk 

Initially, each week a two hour lecture in which the materials are discussed followed by a one hour tutorial in which exercises are discussed. Later, when the course materials are fully developed and tested, we will move to a “flipped classroom” approach. 

End of semester exam - 80% weighting

In-class test (computer cluster) - 20% weighting

Individual feedback for in-class test after marking completed.

Group level feedback for exam after marking completed.

Extensive typeset notes to be provided.