|Unit level:||Level 2|
|Teaching period(s):||Semester 2|
|Offered by||School of Mathematics|
|Available as a free choice unit?:||N
Additional RequirementsMATH20972 pre-requisites
For students on the Actuarial Science and Mathematics programme only.
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.
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.
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.
- Other - 20%
- Written exam - 80%
Assessment Further Information
2.Examination at the end of the semester, two hours duration, 80%
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.
- 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.
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.
- Lectures - 22 hours
- Tutorials - 11 hours
- Independent study hours - 67 hours