Chain Ladder Reserving Methods for Liabilities with Per Occurrence Limits

Motivation: As an insurance regulator, I regularly see instances where maximum limit losses are removed from incurred and/or paid losses prior to application of the development factors. In some of these instances, the triangles and LDFs are created with limited losses, as opposed to unlimited losses.

Method: This paper simulates loss development triangles that include maximum limit losses. It compares exclusion vs. inclusion of maximum limit losses to show how each option affects the accuracy of the results. This paper provides simulated empirical probabilities obtained by randomly dispersing large losses throughout a triangle, then calculating the ultimate limited losses by two different methods.

Conclusion: If limited LDFs are calculated using triangles that include truncated maximum limit losses, then excluding maximum limit losses prior to application of the LDF produces an understated ultimate and reserve.

Availability: Calculations were performed using @RISK Standard version 5.0, from Palisade Corporation, Ithaca, NY, U.S.A. The commercial software package @Risk was used to simulate loss triangles and to create graphs of empirical loss distributions. The Excel/@Risk spreadsheets used for calculating triangles with randomly disbursed large losses are available through the author.

Keywords: Loss development; reserving, data organization, net reserves, gross reserves, ceded reserves, reserving methods, aggregate excess/stop loss; simulation