31.3.2017

UPDATED INFORMATION (16 May 2017)

The planned Seminar "Dependent loss reserving using copulas" by prof. C. Genest  was cancelled due to accute illness of prof. Genest!

We invite you to the seminar on mathematical statistics and its applications entitled Dependent loss reserving using copulas that will take place on Thursday, May 18 at 10:00 a.m. at the lecture hall C of the Faculty of Mathematics, Physics, and Informatics, Comenius University in Bratislava. The Seminar is organized by the Institute of Measurement Science, Slovak Academy of Sciences, in cooperation with the Faculty of Mathematics, Physics, and Informatics, Comenius University. The lecture will be presented by professor Christian Genest from the Department of Mathematics and Statistics, McGill University Montréal (Québec) Canada.

Dependent loss reserving using copulas

Christian Genest

McGill University, Montréal, Canada

In order to determine appropriate reserves and risk capital for incurred but unpaid losses, property and casualty insurance companies must account for the fact that their lines of business may be dependent. For each line of business, payments relating to past claims are usually structured in a run-off triangle arranged to rows according to the accident years, and to columns according to the development periods. Generalized linear models (GLMs) provide a convenient way to capture the influence of these two factors on the distribution of the loss ratios in each triangle. Following Shi & Frees (2011, Astin Bulletin), copulas can then be used to combine these GLMs across lines of business.

To guard against the undesirable effects of an inadequate choice of dependence model on reserve estimation, a two-stage, rank-based inference procedure will be proposed to assist with copula selection and validation in this context. A hierarchical approach will also be advocated for the construction of flexible copulas. As emphasized by Arbenz et al. (2012, Insurance: Mathematics and Economics), this modeling strategy relies on a conditional independence assumption whose implications will be highlighted. Under this assumption, the hierarchical structure can be constructed iteratively using rank-based clustering techniques, as detailed in Côté & Genest (2015, Canadian Journal of Statistics). The entire approach will be illustrated with data for six lines of business from a large Canadian insurance company. This work is joint with Marie-Pier Côté and Anas Abdallah.

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