The effect of reinsurance treaties on the cedent loss reserving

Abstract

Purpose The usual, simple and computationally expensive recovery payment method for a given reinsurance treaty, besides the total run-off triangle, builds a new run-off triangle, say recovery run-off triangle, for the reinsurer’s contribution and predicts the reinsurer’s contribution to the total loss reserves. This paper, without building a recovery run-off triangle, uses the available prior knowledge about a reinsurance treaty to predict the cedent’s loss reserve under five reinsurance treaties. Design/methodology/approach The authors propose a new solution to the problem of how to consider reserving issues when there is a reinsurance treaty for a portfolio of general insurance policies. Considering this when determining pricing or making capital decisions is very important. Findings In particular, it considers the quota share (QS) treaty, surplus (SPL) treaty, excess-of-loss (XL) treaty, largest claims reinsurance (LCR) treaty and excédent du coût moyen relatif (ECOMOR) treaty. Then, it develops a theoretical foundation for predicting the cedent’s loss reserve and evaluating such prediction using the mean square error of prediction (MSEP). The impact of such reinsurance treaties on the variability of the cedent’s loss reserve has been investigated through a simulation study. Originality/value This paper, without building a recovery run-off triangle, uses the available prior knowledge about a reinsurance treaty to predict the cedent’s loss reserve under five reinsurance treaties. In particular, it considers the QS treaty, SPL treaty, XL treaty, LCR treaty and ECOMOR treaty. Then, it develops a theoretical foundation for predicting the cedent’s loss reserve and evaluating such prediction using the MSEP. The impact of such reinsurance treaties on the variability of the cedent’s loss reserve has been investigated through a simulation study.