An actuarial comparison of loss-ratio-Bornhuetter-Ferguson and classical chain ladder techniques in insurance loss reserving: A computational approach

Abstract

An insurance firm promises to reimburse benefits to the insured when unforeseen events evolve. When such contingencies arise, the underwriter has a liability to pay the claim through loss reserving techniques. The estimation of such loss reserving should be technically performed so the insurance firm will not run into a loss. This study aims to (i) estimate the Bornheutter-Ferguson reserve and the inverse of its development factor λn under the aegis of the loss ratio framework. (ii) numerically estimate the chain ladder reserve and final losses, (iii) estimate the Ratio of cumulative payments in successive development periods, and (iv) demonstrate to professional insurance firms how to use these techniques in practice. These techniques evaluated through some run-off loss matrix can be employed to estimate technical provisions for the outstanding claims. Computational evidence from our results over the periods analyzed confirms that on the assumption of 0.9 the loss ratio, the Bornheutter- Ferguson technique as an actuarial extension of the chain ladder method numerically presents a lower reserve value than the corresponding chain ladder reserve, and hence CLreserve=249,811.708>BFreserve=86,612.58.