Insurance Loss Reserving

Sammanfattning: The concept of run-o triangles is widely used within the actuarial eld. Its purpose is to estimate Incurred But Not Reported claims for insurance portfolios, in order to set appropriate reserves that are in compliance with regulatory requirements as well as the company's risk appetite. In this thesis, a parametric approach is proposed, where the portfolios are modeled using non-stationary distributions. The nonstationarity is able to account for various dependencies arising within the run-o triangle. In order to handle negative values, the families within the Generalized Extreme Value distribution have been applied. The ndings are then benchmarked by comparing the method to a non-parametric Chain Ladder bootstrap approach. Using Value-at- Risk and Tail Value-at-Risk measures, the aggregated reserve is then estimated through Monte Carlo simulations by applying elliptical copulas, where the eects from dependence between portfolios are studied. The method is applied on data provided by a Swedish reinsurer, for its portfolios Aviation, Marine and Property. The implementation of the method conveys the impact of model risk and the importance of accurate parameter estimation, otherwise resulting in unrealistic projections. Additionally, dependence for dierent copulas, tail dependence in particular, is proven to have considerable eect for aggregated loss reserving. Keywords: Run-o triangle, IBNR, Non-stationary marginal distributions, Elliptical copulas, Generalized Extreme Value distribution, Value at Risk, Maximum Likelihood Estimation, Chain Ladder.