The Mathematics of Excess Loss Coverages and Retrospective Rating: A Graphical Approach

The mathematics of excess of loss coverages and retrospective ratings involves heavy algebra, mainly because the indemnity payment under such contracts assumes different functional forms in different parts of the loss size distribution. This paper presents a graphical approach to the theory, in which the indemnity payment under various conditions is represented by the regions in a graph described by the cumulative distribution function of the size of loss. Many intricate formulas and relations occurring in the two subjects, some expressible algebraically only in very complicated forms, can be understood simply and clearly through pictures. Treated visually in this paper are many mathematical relations and results included in the examination syllabus. Reinsurance Research - Pricing/Contract Design