Reinsurance Pricing: Excess of Loss and Aggregate

Per-Risk and Per-Occurrence Excess

Per-risk excess of loss covers individual losses above a retention M. The reinsurance pure premium is E[min(max(X-M,0), limit)]. For heavy-tailed distributions, excess layer pricing requires accurate tail modeling using EVT or large-loss data. The increased limits factor (ILF) ratio approach prices layers using ILF(M+limit)/ILF(M). Per-occurrence (catastrophe) excess covers aggregate losses from a single event above a retention, requiring modeling of event-level aggregate losses across affected policies. Reinstatement premiums charge for restoring coverage after a recovery.

Aggregate and Stop-Loss

Aggregate excess covers total losses exceeding a threshold over a period. Pricing requires the aggregate loss distribution, incorporating parameter uncertainty and correlation between risks. The burning cost method uses historical excess losses trended and developed to current levels. Experience rating blends burning cost with exposure rating (from modeled loss distributions). Swing-rated and retrospectively-rated programs adjust premiums based on actual experience within minimum and maximum bounds. Profit commission and sliding scale features link reinsurer profit to cedant results. Exam MAS-II tests excess layer pricing, aggregate distribution computation, and the interaction of reinsurance terms.