31.3.2017
AKTUALIZÁCIA (16.5.2017):
Plánovaná prednáška "Dependent loss reserving using copulas" profesora C. Genesta sa nebude konať pre chorobu prednášajúceho!
Pozývame Vás na seminár z matematickej štatistiky s názvom Dependent loss reserving using copulas,
ktorý sa uskutoční vo štvrtok, 18. mája 2017, o 10:00 hod. v
pocluchárni C Fakulty matematiky, fyziky a informatiky Univerzity
Komenského v Mlynskej doline, Bratislava. Seminár organizuje Ústav
merania SAV v spolupráci s FMFI UK v Bratislave. Prednášať bude profesor
Christian Genest, 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.
References
- Shi, Peng, and Edward W. Frees. "Dependent loss reserving using copulas." Astin Bulletin 41.02 (2011): 449-486.
- Arbenz, Philipp, Christoph Hummel, and Georg Mainik. "Copula based hierarchical risk aggregation through sample reordering." Insurance: Mathematics and Economics 51.1 (2012): 122-133.
- Côté, Marie-Pier, and Christian Genest. "A copula-based risk aggregation model." Canadian Journal of Statistics 43.1 (2015): 60-81.
- Côté, Marie-Pier, Christian Genest, and Anas Abdallah. "Rank-based methods for modeling dependence between loss triangles." European Actuarial Journal 6.2 (2016): 377-408.
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