Overlap Revisited--The `Insurance Charge Reflecting Loss Limitation' Procedure

Several years ago, the retrospective rating plan premium formula was modified with the intention of eliminating "overlap" between its insurance charge and excess loss premium components. Under the modified formula, the excess loss premium is reduced via subtraction of an Excess Loss Adjustment Amount (ELAA). Now, the ELAA approach is likely to be supplanted by an alternative methodology, called ICRLL (Insurance Charge Reflecting Loss Limitation), under which the insurance charge is calculated net of overlap and no adjustment is made to the excess loss premium. ICRLL uses the standard system of equations, modified to correctly reflect the loss limit, along with a column shifting procedure to arrive at a better set of insurance charge values to use for solving the equations. The paper starts with an introductory discussion of overlap and a brief review of the literature. After that, the ELAA methodology is described and its vulnerability to inconsistency is explained and demonstrated. The final section of the paper is devoted to an exposition of the ICRLL procedure. As a topic for future research, the author also presents an alternative "variance matching" approach to the selection of insurance charge values.