Risk Theory II


To know the main principles of premium calculation and its calculation.

To know the main reinsurance treaties and their influence on the aggregate claims.

To calculate ruin probabilities, exact or approximated, in continuous or discrete time for some simple problems.

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.


Asmussen, S. & Albrecher, H. (2010) Ruin Probabilities, World Scientific, Singapore
Bowers, Gerber, Hickman, Jones and Nesbitt. (1997) Actuarial Mathematics (second edition). Itasca, Illinois: The Society of Actuaries
Dickson, D. C. M. (2005) Insurance Risk and Ruin, Cambridge University Press, Cambridge
Kaas, R., Goovaerts, M., Dhaene, J. & Denuit, M. (2008) Modern Actuarial Risk Theory - using R (second edition), Springer
Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999) Stochastic Processes for Insurance and Finance, Wiley

Teaching method

In the theoretical and practical lectures, it will be explained and discussed the successive topics of the course program. The topics are introduced by the teacher, consolidated using as much as possible with real examples drawn from the insurance industry, followed by a brief discussion and use of computational means to support problem solving.
The evaluation consists of two components: two midterm tests concerning the theoretical and applied knowledge. The final classification is the average of the grades in each component, or in the case of fail, it will be the grade of the final exam.

Evaluation method

T1 Premium Principles and Reinsurance (60%), T2 Ruin Theory (40%)

Subject matter

  1. Premium principles

    1. Utility theory

    2. Premium calculation principles

    3. Properties

  2. Reinsurance

    1. Quota share reinsurance

    2. Surplus reinsurance

    3. Excess of loss reinsurance

    4. Stop loss reinsurance

  3. Ruin theory

    1. Continuous time model (the adjustment coefficient, ruin probability, Lundberg’s inequality, maximum aggregate loss, approximations to the ruin probability)

    2. Discrete time model (the adjustment coefficient, ruin probability, Lundberg’s inequality)

    3. The impact of reinsurance


Programs where the course is taught: