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

The mathematics of excess of loss coverages and retrospective rating involves heavy algebra, mainly because the indemnity payment under such contracts assumes different functional forms in different parts of the loss size. This paper presents a graphical approach to the theory, in which the indemnity payment under various conditions is represented by the areas of regions in a graph described by the cumulative distribution function of 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 the pictures. Treated visually in this paper are many mathematical relations and results included in the examination syllabus.