A Chain-Ladder Analysis of P&I Claims

Abstract

This article applies chain-ladder methods to the reserving of marine P&I claims. Starting from reports that International Group pool claims had reached an all-time high at the halfway point of a claims year and that a ratings agency expected almost every club to seek higher pricing at the next renewal, the author notes that insurers sell promises whose cost is unknown in advance, so that reserves for outstanding claims and for losses incurred but not reported (IBNR) are often the largest liability on an insurer’s balance sheet. The analysis, carried out in R, uses a development triangle of the estimated cost of notified pool claims for the origin years 2010/11 to 2019/20 and applies the classical deterministic chain-ladder method together with the Mack and Bootstrap chain-ladder methods. The loss development factor was estimated at 1.059312, above unity and higher than the 1.0127889 of the previous period, indicating an increasingly positive trend for IBNR. The predicted ultimate claim was 33,436 under the chain-ladder method, 31,564.58 under the Mack method and 31,430 under the Bootstrap method, with IBNR reserves of 1,487.58 and 1,353 under the Mack and Bootstrap methods respectively. Because the coefficient of variation of IBNR was 221%, the Bootstrap method was followed. The results are consistent with a general increase in rates at the 2021 renewal.

Abstract prepared by the editorial office from the full text of the article; the authors did not supply one.