Risk Theory II
Objectives
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
Code
12459
Credits
6.0
Responsible teacher
Rui Manuel Rodrigues Cardoso
Hours
Weekly  3
Total  48
Teaching language
Português
Prerequisites
The students should be provided with knowledge about calculus, numerical analysis, probabilities and statistics.
Bibliography
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

Premium principles

Utility theory

Premium calculation principles

Properties

Reinsurance

Quota share reinsurance

Surplus reinsurance

Excess of loss reinsurance

Stop loss reinsurance

Ruin theory

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

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

The impact of reinsurance