Outward Reinsurance of Long Tail Liabilies- Some Suprising Findings

by Prof Ben Zehnwirth and Dr. Glen Barnett

Abstract

Traditional covers include risk transfer of individual risk excess of loss and Adverse Development Cover (ADC), both retrospective and prospective. It is expected that the coefficient of variation of the cedant's reserves net of reinsurance is less than the coefficient of variation of gross reserves. Surprisingly, this may not be the case for individual excess of loss.

That is, the percentage capital required in excess of the mean of the net reserves is not necessarily lower than the percentage capital required in excess of the mean of the gross reserves, for any percentile. Such a reinsurance arrangement is tantamount to proportional reinsurance in its impact. This is far from optimal for the insurer. This effect is often observed prospectively as well.

We show how to design composite models for triangles that represent different layers and also composite models for net (of reinsurance) and gross triangles. These composite models, inter alia, quantify correlations between the different layers (segments). Some of the findings, such as highest correlations between nearest neighbours, are not surprising, while other findings are more surprising. The approach can also be used to assess whether reinsurance programs that have been in effect for many years are 'effective' for the insurer. Quite often the answer is no!