Index clause: analytical properties and the capitalization strategy

In non-life insurance, some bodily liability losses (e.g. loss of income) are paid out as annuity until specified age or death of victim. In case of excess of loss reinsurance, reinsurers often do not accept the inflation risk embedded in such losses and therefore include in the reinsurance treaty so called index clause which increases the priority by the impact of the inflation on the loss. A formula to calculate the expected reinsurance recoveries and its limiting behavior in case of presence of the index clause is derived and illustrated. A capitalization strategy which minimizes the insurer’s loss is derived.