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Risk Theory

Unit code: MATH39542
Credit Rating: 10
Unit level: Level 3
Teaching period(s): Semester 2
Offered by School of Mathematics
Available as a free choice unit?: N



Additional Requirements

Actuarial Science only


This unit aims at providing students with a further grounding in the important statistical and probabilistic techniques and models relevant to the non-life insurance industry.


Following up on the course unit Actuarial Insurance this unit introduces further concepts and models relevant to the non-life industry, in particular the important concept of ruin in a risk model is discussed.

Learning outcomes

On completing this course unit students will be able to:

  • in the context of statistical inference, compare and contrast the Bayesian approach and the frequentist approach,
  • describe the Bayesian approach to Decision Theory and relate the concepts Bayes risk, Bayes rule, posterior risk and risk function,
  • determine the optimal action or decision function for a given decision problem using the Bayesian approach,
  • in the context of Bayesian statistical inference, evaluate Bayes estimate for the unknown parameter,
  • discuss the assumptions and goals of Credibility Theory, and compute the types of credibility estimates seen in the course,
  • describe the premium principles and their desirable properties seen in the course, and (dis)prove whether a premium principle satisfies one of these desirable properties for examples of similar difficulty as seen in the course,
  • discuss the elements making up Cramer-Lundberg model and the Net Profit Condition,
  • evaluate the probability of ruin in a Cramer-Lundberg capital process for examples of similar difficulty as seen in the course,
  • discuss the key idea in the proof of Lundberg’s inequality and apply it to a Cramer-Lundberg capital process,
  • explain how reinsurance can be incorporated in the Cramer-Lundberg model and determine the optimal level of reinsurance for examples of similar difficulty as seen in the course.


Assessment methods

  • Other - 10%
  • Written exam - 90%

Assessment Further Information

  • Coursework 10%
  • Examination at the end of the semester, two hours duration, 90%.


  1. Risk models. Several models, probability and consequences of ruin, Cramer-Lundberg.
  2. Premium principles.
  3. Bayesian statistics.
  4. Credibility Theory.

Recommended reading

  • Core Reading: Subject CT6, Statistical Methods. Produced by the Actuarial Education Company (www.acted.co.uk).

Feedback methods

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.

Study hours

  • Lectures - 22 hours
  • Tutorials - 11 hours
  • Independent study hours - 67 hours

Teaching staff

Kees Van Schaik - Unit coordinator

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