ST348-15 Risk Theory

Introductory description

This module runs in Term 2 and is available for students on a course where it is a listed option. It is not available as an Unusual Option to students with their home department outside Statistics.

Co-requisite: ST318 Probability Theory.

Results from this module may be partly used to determine exemption eligibility in the Institute and Faculty of Actuaries modules CM2, CS1, and CS2. (Independent application with the IFoA may be required to receive the exemption.)

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Decision theory and Bayesian estimation.
Loss distributions and resinsurance contracts.
Aggregate claims distributions.
Introduction to copulas.
Ruin theory.
Simple models for credit risk.
Run-off triangles.
Generalized linear models.
Time series.
Simulation of a stochastic process.

Learning outcomes

By the end of the module, students should be able to:

• Know how probability models are used in general insurance.
• Understand the concept of methods of re-insurance to hedge against risk.
• develop the mathematical skills and statistical techniques of particular relevance to general financial work and insurance.
• calculate central moments of claim distributions (with limits and risk sharing arrangements).
• calculate insurance premiums and reserves, as well as derive Bayesian estimators and credibility premiums.
• study other professional actuarial subjects in the Core Application and Specialist Technical areas.

Indicative reading list

P.J. Boland (2007) Statistical and probabilistic methods in actuarial sciences.

C.D. Daykin, T. Pentikainen, M. Pesonon (1994) Practical Risk Theory for Actuaries.

S.A. Klugman (1985) Loss distributions.

P. McCullagh, J.A. Nelder. (1989) Generalized Linear Models. Chapman and Hall, London.

View reading list on Talis Aspire

Subject specific skills

• Evaluate mathematical and/or statistical techniques.
• Create structured and coherent arguments communicating them in written form.
• Construct and develop logical mathematical arguments with clear identification of assumptions and conclusions.
• Communicate subject-specific information effectively and coherently.
• Evaluate data/problems, including potentially conflicting or incomplete information, abstract essential information and formulate an appropriate analysis/solution strategy using appropriate mathematical language and pursue these strategies through a complete solution cycle.

Transferable skills

• Critical thinking: extracting patterns from incomplete data and using them to form evidence-based conclusions.
• Problem solving: use of logical reasoning to build arguments grounded in evidence and with explicit underlying assumptions.
• Self-awareness: monitoring of your own learning and seeking feedback.
• Communication: verbal discussion of ideas in seminars and among peers; written communication in assignments and the final project.
• Information literacy: evaluation of data and uncertainty in a model-based way.
• Digital literacy: use of computational tools to understand and visualise data, and to produce reports. - Professionalism: self-motivation, taking charge of your own learning, and prioritising effectively.
• Ethics: reflect on professional responsibilities as a statistician in conjunction with the generation and dissemination of information.