The data are taken from a French Insurance Company.
The paper applies some new techniques, invented by Gary Venter, which allow to select the more appropriate copula among a set of copulas.
A few functions are introduced in order to highlight different properties of the various copulas. As these functions can also be approximated from the data, they are used to assess which copulas more closely capture features of the data.
Thanks to this, we are able to demonstrate that the dependence structure between “motor” and “fire” insurance can be described with the HRT copula (also called the Clayton “survival copula”). This copula has low correlation in the left tail but high correlation in the right, ie for large losses.
Firstly we estimate the copula parameter without any assumption on the parametric shape of the marginal distributions.
The same procedure as in the Klugman-Parsa paper “Fitting bivariate loss distributions with copulas” is also used.
Parameters of the bivariate distribution (two for each marginal and one for the copula) are also estimated with a MLE technique. Goodness of fit tests are performed.
The main difference with Klugman-Parsa paper is that our model is not a “ground-up model”. The marginals which are linked by the copula are only defined above a certain amount in each line of business. Thus we may achieve greater accuracy in the tail of the distribution.
Parametric estimation is used to derive some reinsurance premiums. Keeping the same HRT dependence structure, we change the dependence coefficient to evaluate its impact on the premium of different reinsurance contracts.
Keywords:copulas,windstorms,reinsurance
Paper is written in French.
