Some reflections on different disability models

Abstract

As a retired actuary of life and health insurance the author has wished to summarize his experience and reflections about different systems of disability insurance. He wants to show how the premium technique of the “classic” Hamza process presented in 1900 as a model of the invalidity insurance technique without any element of recovery can be described for an active person by three alternative formulas of expected value of a disability indemnity. His of interest to observe that the second of these formulas can be applied to the technique of sickness insurance based on the probability of being sick. This technique is also used in British and Norwegian long term disability insurance. The third formula leads after modification to the Swedish sickness annuity technique and, further, to the technique of basic continuance tables used in U.S.A. In describing the classic process the author has used the discontinuous approach, but otherwise the continuous approach with integrals instead of sums has been preferred.

Methods of calculating the premium for “waiver of premium” have in this paper only been touched upon as a result of a modification of the sickness annuity technique. It has been found necessary to refrain from the opportunity to illustrate the interesting development of the invalidity technique according to Schoenbaum and later to Simonsen who introduced a series of transition probabilities between different states of activity and disablement.