“Estimating incurred claims”

Extract

Mr. Benedikt uses “chain relatives” based on the incurred claim totals included in Part 5 of Schedule “P” of the annual statement required for fire and casualty companies in the United States. Each total is for the losses as developed to end of calendar year (j) for claims incurred because of accidents in calendar year (i). Each total is the sum of the actual payments made before the end of year (j) plus the reserve for estimated payments to be made after the end of year (j) for claims incurred in year (i). The “chain relatives” are ratios. The “chain relative” a_i,j is the ratio of developed losses to end of (j + 1) to the developed losses at the end of year (j).

Each total of Part 5 of Schedule “P” equals the sum of the total payments to date plus the total reserves for future payments for the corresponding classification of claims. Separate totals for these amounts are given in Part 1 of Schedule “P”. The totals of Part 5 are not secured directly from Part 1 because Part 1 gives totals by policy year of issue only and Part 5 separates the totals by policy of issue by calendar year in which claims are incurred. The two parts are prepared from the same basic claim information and agree in total.

The accumulated total paid losses for most casualty lines increase with passage of time. This accumulated total for paid losses can be reduced only if there are recoveries for losses previously paid, such as can occur for auto collision. For auto collision, the insurance company for this insurance can pay the insured for the damage to his car and then later recover from the insurance company that provided the liability insurance for another car involved in the same accident. Such substantial recoveries normally do not occur for auto liability insurance for bodily injury and property damage.