Abstract:
Insurance companies maintain different lines of business as a mode of diversification
which in itself aids in reducing risks of encountering ruin. The dependence structure
of these lines of business cannot be ignored especially in rate making as it reduces
diversification benefits. However, in practice you would find that risks are more
heterogeneous than homogeneous a problem that can be solved by breaking down
the risks into a number of homogeneous categories. The lines of business are considered,
here, to contain sub-classes which are homogeneous. The lines will depict a
hierarchical structure from the sub-classes to the main lines of business up to the
portfolio level and their dependence structure is studied here by the hierarchical copulas.
In risk classification, similar risks should be assigned to the same class with
respect to each variable. The dependencies are examined by fitting copulas, estimating
the dependence parameters and lastly using distance matrices to cluster the
risks together. The distance to use in the classification is determined by the problem
at hand. The empirical study derives its data from the general insurance business
in Kenya where the risks are classified by the Copula based approach. This work
proposed the use of the upper tail dependence, measured by the tail index, derived
from the dependence parameter in determining the retention limits for a re-insurance
arrangement. Though the dependence is not the only factor to consider for such reinsurance
treaties the forwarding proportions should be some where proportional to
1/(1 − Tail index). This will ensure that the highly dependent risks in the upper tail
will forward higher proportions to the re-insurer and vice versa.
