Risk Theory I


To have knowledge of the mais distributions in Non-life Insurance. To know the characteristics of the risk models and apply them. To calculate the exact or approximate probabilities related to aggregate claims.

General characterization





Responsible teacher

Maria de Lourdes Belchior Afonso


Weekly - 3

Total - 48

Teaching language



The students should be provided with knowledge about calculus, numerical analysis, probabilities and statistics.


  • Bowers, Gerber, Hickman, Jones and Nesbitt. (1997) Actuarial Mathematics (second edition). Itasca, Illinois: The Society of Actuaries

  • Yiu-Kuen Tse.(2009), Nonlife Actuarial Models:Theory, Methods and Evaluation,Cambridge University Press, Cambridge

  • Kaas, R., Goovaerts, M., Dhaene, J. & Denuit, M. (2008) Modern Actuarial Risk Theory - using R (second edition), Springer

  • Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012) Loss Models: From Data To Decisions (fourth edition), Wiley

  • David Bahnemann (2015) DISTRIBUTIONS FOR ACTUARIES, CAS MONOGRAPH SERIES NUMBER 2 Casualty Actuarial Society

Teaching method

The problem-solving sessions allows an immediate connection between theoretical concepts and their applicability.

In the first part of the class the theoretical concepts are introduced. The second part is complemented with problems solving in paper and computer. This way, the students have an integrated view of the topics taught, fostering critical thinking and teamwork. 

The class work is supplemented with exercises. Students have additional support in their study with support material (transparencies, theoretical notes and solved tests), or with extra tutorial time.

The objectives achievement is assessed on a continuous basis or through the execution of a final exam. The evaluation components are tests, practical assignment and/or final exam.

Evaluation method


It is provided by the TP Presentation.

The TP is carried out in groups of 2 and is evaluated in three components (the results, the report, the oral presentation with equal weight).

Approval in continuous assessment:

The evaluation in normal season consists of: 2 tests and 1 practical work to be done during the class period. Let T1 , T2 and TP be the scores obtained, respectively, in both tests and in the practical work. Let AC=0.3*T1+0.4*T2+0.3*TP be the classifications obtained at the regular season. The student is approved in the regular season if AC>=9.5

Failure to carry out any component implies a zero grade in that component, for the calculation of AC.

Approval on appeal:

Let E exam grade.

Let NR = 0.7 E + 0.3 TP be the final grade. The Student approves if NR>=9.5

Grade improvement:

Students may carry out the exam, with a view to improving their grade. The practical assignment cannot be improved.

Grades equal or higher than 17.5 may be suject to additional assignment.

Subject matter

Claims Distribution.

Individual Risk Model.

Collective risk model.

The distribution of aggregate claims.


Programs where the course is taught: