The Effect of Trend on Excess of Loss Coverage

The subject of the effect of trend on excess of loss coverages has been addressed quite frequently in the Proceedings over the years. Several authors have made the point that with a fixed retention and uniform trend by size of loss, expected excess losses increase proportionally much more than indicated by the general rate of inflation. This is certainly true when considering uncapped excess losses, but it may not be true when considering a specific layer of excess losses. This is because just as the effect of inflation is leveraged at the retention, it is dampened at the upper limit of the layer. This paper uses graphs to examine how the leveraging effect and dampening effect combine to affect layers of excess losses. This particular issue has historically received very little attention in the Proceedings. The paper begins by examining the excess layer trend factors of a typical loss distribution, and then proceeds to demonstrate how changing each of the two parameters of this distribution affects the trend factors. The paper then looks at the effect of changing the type of distribution. Finally, the paper examines the effect of introduction g the concept of varying trend by size of loss. Reinsurance Research - Loss Distributions, Size of; Increased Limits/Excess of Loss