General Insurance

MATH69531 General Insurance 15 Semester 1 Postgraduate Taught Level 6 Kees Van Schaik Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 This course gives an introduction into the mathematical techniques used in the field of non-life insurance (also referred to as general insurance). As the name implies, non-life insurance concerns all insurance products that are not dependent on the customer's survival or death. This concerns for instance the insurance of objects such as your bike and your car, travel insurance, accident insurance, fire insurance etc. For comparison, products such as pensions are life insurance rather than non-life insurance products. We will mainly be involved with building and analysing stochastic models to make predictions about how many claims the insurance company should expect in the future for a certain portfolio of non-life insurance products, and how large these claims are. This is important to determine how much income the insurance company should generate, in the form of premium payments received from its customers, in order to be able to deal with the incoming claims, make a bit of profit as well and still not charge such high premiums nobody would be interested in buying the product. The course MATH69542 Risk Theory in semester 2 further builds on the work done in this course. This course gives an introduction into the mathematical techniques used in the field of non-life insurance (also referred to as general insurance). As the name implies, non-life insurance concerns all insurance products that are not dependent on the customer's survival or death. This concerns for instance the insurance of objects such as your bike and your car, travel insurance, accident insurance, fire insurance etc. For comparison, products such as pensions are life insurance rather than non-life insurance products. We will mainly be involved with building and analysing stochastic models to make predictions about how many claims the insurance company should expect in the future for a certain portfolio of non-life insurance products, and how large these claims are. This is important to determine how much income the insurance company should generate, in the form of premium payments received from its customers, in order to be able to deal with the incoming claims, make a bit of profit as well and still not charge such high premiums nobody would be interested in buying the product. The course MATH69542 Risk Theory in semester 2 further builds on the work done in this course. The unit aims to provide students a grounding in modern stochastic modelling techniques of particular relevance to general non-life insurance. On completion of this unit, successful students will be able to: <ul> <li> Evaluate and construct (joint) distributions, moments, generating functions and dependenceof random variables, with appropriate use of R.</li> <li> Construct algorithms for simulating samples from distributions and implement these in R.</li> <li> Analyse data sets using R</li> <li> Construct and evaluate point estimators, hypothesis tests and interval estimators for Statistical Inference problems, with appropriate use of R</li> <li> Describe a Linear Model and execute the procedure of fitting a Linear Model to a given dataset (also in R)</li> <li> Assess the suitability of a Linear Model for analysing a given data set, with appropriate use of R</li> <li> Describe a Risk Model and discuss its applications in insurance</li> <li> Analyse and evaluate the properties of the random aggregate claim amount in a Collective Risk model</li> <li> Evaluate several forms of parameter dependence, such as reinsurance, in a Risk Model.</li> </ul> <ul> <li> Revision of Probability Theory</li> <li> Data analysis</li> <li> Statistical inference: point estimation, hypothesis testing and confidence intervals</li> <li> Linear Models</li> <li> Loss distributions in insurance: parametrized families of loss distributions, reinsurance, and estimation of the parameters</li> <li> Risk models (1): the collective risk model. Modelling the claim number process, the aggregate claim amount. Properties of the aggregate claim amount. The compound Poisson model and the compound Binomial model</li> <li> Risk models (2): several forms of reinsurance in the collective risk model</li> <li> Risk models (3): approximations of the aggregate claim amount (CLT and others).</li> </ul> 0 Other 100% <ul> <li> Coursework 100% (four pieces take home coursework, weights 20%, 30%, 20%, 30%).</li> </ul> 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.   N Probability and Random Processes. Grimmett, G. and Stirzaker, D. (ISBN: 0198572220)Mathematical statistics with applications. Mendenhall, W. and Wackerly, D. (ISBN: 0495110817)Insurance Risk and Ruin. Dickson, D.C.M. (ISBN: 9780521176750) Lectures 26 Tutorials 12 0 112 This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates.