Daniela Escobar

This course is available on the MSc in Financial Mathematics, MSc in Quantitative Methods for Risk Management, MSc in Statistics (Financial Statistics) and MSc in Statistics (Financial Statistics) (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.

The course is available with permission when students meet requirement on pre-requisities. 

Students must have completed Stochastic Processes (ST302) and Probability, Distribution Theory and Inference (ST202).

Good undergraduate understanding of distribution theory and stochastic processes. ST202, ST302 or their equivalent.

A self-contained introduction to insurance risk analysis. Starting from classical actuarial modelling of insurance risk, utility theory with optimal forms of insurance from the insured's and from the insurer's point of view are analysed. Pareto-optimal risk exchanges are introduced. Standard schemes of reinsurance are introduced and analysed. The individual and collective model are introduced to understand the aggregated claim process and approximate it. There is an emphasis in the compound Poisson process and therefore a detailed description of the Poisson process is explained. In the second part of the course we cover Ruin theory for an insurance company and capital requirement are studied. Heavy tail distributions and the extreme value theory are introduced. We solve reinsurance problems in a scheme with aggregated claims. Finally, we study closed-form solutions of the ruin probability as we also approximate it using R.

20 hours of lectures and 10 hours of seminars in the AT.

Week 6 will be used as a reading week.

Students will be expected to produce 6 problem sets in the AT.

Kaas, R., Goovaerts, M., Dhaene, J., & Denuit, M. Modern actuarial risk theory: using R 

Thomas Mikosch, Non-Life Insurance Mathematics

Ragnar Norberg, Non-life Insurance Mathematics (Lecture notes)

Pauline Barrieu, Luca Albertini, The Handbook of Insurance-Linked Securities

Exam (70%, duration: 2 hours) in the spring exam period.
Project (30%) in the WT.